Character tier list by importance of aiming and mouse skill. This is a rough guide to who will be easier to play for the majority of players:
Bottom: Mercy, Reinhardt, Torbjorn, Symmetra
Low: Lucio, Winston, Bastion
Medium: Junkrat, Reaper, D.Va
High: Mei, Zenyatta, Roadhog, Zarya
Higher: Pharah, Hanzo, Tracer, Genji
All About Aim: Widowmaker, Soldier 76, McCree
What heroes to start with:
Which heroes to try first depends on the map. There's 3 situations. On 9 maps you can be either offense or defense. The other 3 maps (nepal, ilios, lijiang tower) are King of the Hill where it's a symmetric fight.
Defense: Try Torbjorn first because his turret aims by itself and he can be really strong for a new player. Build his turret towards the back where it'll fight once the enemy team comes in and attacks, but they won't be able to kill it easily from a distance. Putting it around a corner the enemy team will come through can work well. Then try Symmetra, Bastion and Junkrat who are also defensive specialists that you can be effective with quickly without amazing aim.
Offense: Try Winston on teams with another tank (it's too much pressure on you if you're a solo tank). More advanced characters to try later on are Zarya (with another tank) or Pharah.
King of the Hill: Try Winston then Reaper to shoot people at close range. Zarya works here too if you've gotten comfortable with her already.
Every map: Try Lucio and Mercy on teams with another healer (as solo healer it's too much pressure on you until you get used to playing them). Lucio is preferred on King of the Hill maps and Mercy on other maps, but both are fine. Roadhog is reasonably easy to use, but at first try to have another tank on the team so you aren't under the pressure of doing all the tanking alone.
Focus on learning a small number of characters. These are suggested characters to try out. Try them and see which ones you like more and less. Then pick some to focus on. Don't play them all. If you focus on a few characters you will be able to get good with them faster. 3-5 would be a good number of characters. Try to pick one character for each type of map so you always have someone good to use. Picking one character from each of the in-game labels (Offense, Defense, Support, Tank) would be reasonable, too. You could even start with only 1-2 characters if you're careful to pick flexible characters.
Duplicate heroes can be a problem: don't use a third copy of any hero on your team. Never use two Symmetras. Don't use 2 snipers (hanzo and widow are both snipers). Initially, avoid doubles of any hero except Mercy, Lucio, Zenyatta, Winston, Roadhog, Torbjorn.
All teams need to have a healer and a tank. Symmetra is a "support" but not a healer. D.Va is not really a tank and cannot be your only tank. Having two tanks is recommended unless your tank is Reinhardt in which case one tank is fine (D.Va can count as one of your two tanks). Having two healers is generally recommended but they're the least popular so you'll frequently only have one. Zenyatta heals less than Mercy and Lucio, so Zenyatta doesn't work as well as a solo healer. Note that some characters can reduce the pressure on the healer(s), especially Soldier 76 and Symmetra, and also anyone with a self-heal ability.
Don't use Torbjorn, Symmetra, Bastion, or Junkrat on offense or king of the hill.
Don't use a sniper on king of the hill maps. Don't use snipers on offense at first. The way people start with snipers is you find a spot in back and then wait for someone to come in view for you to snipe, and that only works on defense. However, as you improve, both sniper characters can actually be pretty mobile and work on offense too.
If you want a high damage hero with good range, try Pharah. Her rockets do area of effect damage, so your aim doesn't have to be as exact as some of the other long range heroes. However she's harder to use effectively than the starter heroes I suggested above. If you play Pharah, don't fly around all the time. The majority of the time, Pharah should stay on the ground and play like a normal hero. Use your jetpack to fly at key moments when the enemy is under pressure. Flying generally makes it so the entire enemy team can shoot at you, so you will die fast if the enemies aren't already really busy in a brawl with the rest of your team.
Set your mouse sensitivity in controls before you play. You want to get a good setting and then get used to it. Each time you change it you have to relearn some of your mouse skill. Here's how to get started: spin your character's view around in a full circle. So put your crosshairs on something then move your mouse sideways so you spin until you see the crosshairs on the same thing again. You can measure the mouse movement distance for this and it's called inches/360. Set it so that it's around 80% of the width of your mouse pad. In regular gameplay you want to be able to spin around half way (180 degrees) to see behind you. This will make a 180 take a little less than half your mousepad so you can still do a 180 even if your mouse is a little off center. (If you have a small mousepad, you may also want to consider getting a larger one meant for gamers.) This will make your mouse slower than a lot of people are used to, but will improve your ability to aim.
Reinhardt is pretty easy to control, but he's very central to the team. Playing him puts pressure on you similar to being a solo tank even if you have another tank on the team. Wait to try Reinhardt until you have a reasonable understanding of what's going on in the game. And when you play Reinhardt please don't use your charge ability to leave your team behind and suicide into the enemy team.
Symmetra is bad when defending the last area of the map before you lose. At that point, your teleporter won't do much. Change heroes after a death when you're defending the last area. Also when playing Symmetra you need to focus on staying alive. Your big goal is to get a teleporter up before your first death.
With Roadhog, after you hook someone you should hold down left click to shoot them in the head as soon as possible, and then hit Quick Melee for an extra 30 damage immediately after shooting.
Soldier 76 has good range but doesn't do his best work in close up brawls. He does best on high ground near some cover, a bit towards the back. At longer ranges do burst fire with his gun (if you just hold it down constantly the bullets start scattering a lot and losing accuracy, but if you shoot around 4-5 shots at a time and then stop shooting for a moment then he can maintain great accuracy at long range). Soldier 76's bullets hit instantly with no travel time. He's a pretty difficult hero to use because his damage really depends on how well you aim.
Some people think McCree is a flanker who fights at short range. This is incorrect. McCree's gun has perfect accuracy and hits instantly at any range, so he's actually one of the best long range shooters. He's also good at close range duels too thanks to his flashbang. McCree is hard to play because really amazing aim makes a huge difference. If you do try him, please stay grouped with your team most of the time.
Zarya is best on offense for taking capture points or pushing the payload to the final end point. The reason is Graviton Surge is a great ultimate ability for getting a team wipe. On Hanamura, Volskaya and Anubis the offense can win the game by winning only two team fights. Two good Graviton Surges can win the game! Graviton Surge excels at winning a teamfight to make progress at the tough spots where you might otherwise get stuck.
The key to playing Winston is to hang back and then jump in when your team fights. Never jump in alone or you'll just die to their whole team. And don't hang out in the middle towards the front of your team. With your short range you won't accomplish much, and with your big size people will shoot you. Winston has to either commit hard to a fight (which needs to be at the same time your team fights) or else don't fight at all. Winston is either in or out. (After fighting for a while, if your team is losing or you're running out of health, then it's fine to use your jump ability to run away.)
Lucio's speed and healing auras don't stack if you have 2 lucios. If both lucios are alive in the same place, one should use healing and the other use speed.
Play extra defensively when you are Mercy and have resurrection ready. You can even stop healing sometimes to stay safe around a corner if a big fight is happening and you need to make sure you live long enough to resurrect everyone.
Lucio's Sound Barrier and Mercy's Resurrect both benefit a ton from your team grouping up. Talk to them! Use the 'Z' hotkey to announce your ultimate is ready and use the Group Up communication too.
If people on your team die, try to regroup in a safe, conservative position. Don't just run in and die once the fight turns against your team too much. While waiting around to regroup, use that time to talk to your team!
Don't flank when you're new. Just stay with your team. Flanking is an advanced tactic which will hurt your team if it isn't done right. Just make sure to pick heroes that are good in the team instead of flanking heroes (tracer, genji, reaper). The flanking heroes can play with their team more normally on the King of the Hill maps, but avoid them on offense and defense for your first 100 levels or longer.
If you're the only healer or tank, switching heroes can screw your team over. Either don't switch that game or, if you want to switch, type a chat message telling your team that you're switching and someone else needs to switch too in order to take over healing or tanking for you. If you switch heroes in a way that messes up your team setup without communicating with your team, you are screwing your team over.
Try not to switch heroes when your ultimate is at 75% or more charge. It's most efficient to switch after a death with your ultimate at 25% or less charge.
On characters with slower attacks like pharah and mccree, shoot each shot individually, don't hold down left click.
V is a bad default hotkey for Quick Melee. Change it to F (easier to reach) and/or a mouse button.
Put the Effects and Model Detail graphics settings to Low. This removes some clutter so it's easier to see what's going on. For the other settings, just make sure you get plenty of frame rate (if you ever drop under 70 fps that's pretty bad).
If you play Widowmaker, go to the controls settings for her specific character and set the zoom scoped sensitivity to exactly 0 (zero). In short that makes your mouse act normally so you don't have to learn two different ways of using your mouse.
Set your crosshair color to green so it's easier to see. I also recommend setting the Short Crosshair option for all characters. You should keep Bloom enabled initially to see how it works, but then disable it for everyone except Soldier 76. Bloom makes your crosshairs expand, in order to show when your character's gun is less accurate. (Some guns are less accurate after you shoot multiple times in a row).
If you're missing lots of shots, definitely stay away from the final two tiers of characters on the aiming difficulty list. And don't play Zenyatta either because if you aren't hitting many shots with him then he's clearly inferior to Lucio and Mercy.
Feel free to try any character if you want for a game or two and see how it goes.
With any character, if it's really not working, just switch to another character mid game. You can try them again another time with different allies and opponents.
Some of these tips won't apply to you if you've already got great aim from playing another shooter like Counterstrike or Team Fortress for many years. The game also changes if you have a group of 6 good players who know each other, plan out strategies in advance, specialize with specific heroes for their team, talk on voice chat, and work as an organized team.