What’s the best "2 muscles per day" split for someone stuck with a 45-min gym window?

I’m currently focusing on a body recomp (trying to lose fat and build muscle at the same time) and I find that full-body workouts take way too long in our crowded local gyms. I want to switch to a 2-muscle group per day schedule so I can get in and out in under an hour.

​My questions for you guys:

1)​What are your favorite pairings for a 2-muscle split?

2)​Should I prioritize the big muscle first in the session?

3)​How do you manage your energy if you're working out before/after a long shift or university?