I usually do philosophy first when I wake up, when I'm fresh. This works for me because I'm not sleep deprived. Lots of people have a hard time in the mornings because they are chronically sleep deprived. Getting enough sleep is important to being a good thinker. I wake up without caffeine, an alarm, a shower, or anything to wake me up. I don't keep track, but I'd guess that I average over 8 hours of sleep per day (including naps).
I don't eat until after doing philosophy. (I find I'm not hungry for at least 4 hours after waking up.) When convenient, I use eating, exercising or showering as a break after doing morning philosophy.
Happily, I do contract software work from home and can choose my own hours to work. So I can do philosophy first regardless of what time I wake up, then do software work or whatever else later on. My sleep and wake times vary significantly and sometimes I take naps. I sleep when I'm tired, not on a schedule.
I avoid scheduling many activities. And I get a lot of stuff delivered, including lots of my groceries, so I don't need to go places during business hours much. This improves my sleep and gives me the flexibility to do what I want when I want to.
If I worked a 9-5 job, I would go to sleep by 8pm so I could wake up by 4am and do philosophy in the morning before work.
If you work a regular job, and you want to be a better thinker, I recommend you try something like this. Don't wake up for work. Sleep after work and then wake up long before work. Then you can do your own thing (e.g. study critical thinking skills and read philosophy books) when you're fresh. This can also work with anything intellectual, e.g. if you're writing a novel. It's really hard to do your best thinking after an 8 hour workday.
There are some problems you may run into:
1) Missing new TV shows. You should record your shows for watching later, or buy or torrent them online. You don't have to watch TV shows when they air. If people at work will discuss the show the next day and you want to join the discussions and avoid spoilers, consider watching in the morning. E.g. do philosophy from 4-7:30am, then watch the TV show (while eating breakfast) then go to work.
2) Social life. If you care more about socializing than thinking, you'll want to be available in the evenings when our culture prefers to do social activities. You've gotta choose. You can't be a productive, great thinker; work a regular job; deal with life (load the dishwasher, go to the dentist, etc); and also keep up a conventional social life. There isn't time for all that.
3) Family time. If you need to stay up until midnight to have enough time with your kids and spouse after work, then you aren't going to have enough time for intellectual activities regardless of your sleep schedule. That's your choice. Good luck trying to squeeze in some thinking on weekends, I guess, but that's when you'll be busy going places and doing family and/or social activities that don't fit on weekdays.
4) I need to be at my best at work. If you're especially smart (like most people interested in my blog who want to be intellectually productive outside of work) then you can do most jobs just fine without being at your very sharpest. You aren't being paid extra to work right after sleeping (actually lots of people come in tired in the morning because they're sleep deprived, and that's perfectly acceptable at most jobs). If you're struggling at work, then OK focus on that but don't expect to be very productive on an intellectual side project. But don't give up your own stuff to try extra super hard at work when you're already doing fine, that'll just get you exploited more than rewarded.
Real talk: If you work full time and have a family life and a social life, you're probably sleep deprived already. You've chosen how to spend your time. On the other hand, if you want to do some kind of thinking or creative pursuit, and you're willing to allocate time for it, then try changing your sleep cycle so you can do it in the morning before work, while fresh, instead of trying to do it after work.
All of this applies if you go to school rather than work. And if you don't work, then try getting enough sleep and doing your most intellectually demanding activity first thing after waking, when you're the freshest.