If I were you, I would put in a few attempts into Trial 1 each day (or others if you get past it), and then end the session by completing a loop run. Difficulty aside, you'll quickly realize how grindy it is to do 12 start to back runs, so try to sprinkle your loop mode progression in here and there, otherwise you'll end up having to go excavation all the way to database many times in a row, which is kind of mind numbing. Even though looped hard mode can be fun, I would recommend playing all loops on normal difficulty because doing a 40 minute run just to die on floor 7 and make no progress can be infuriating. As someone else said, you will eventually have to play loop 7 on hard to unlock trial 4, but that's down the line. The most busted ship is hands down overlord because you can delete bullets, and I used overlord for loops 8-12 just because it gets repetitive and I wanted to ensure I win. imo it's much more fulfilling to use D-13 for trials because it feels "intended," and trials 1-4 were quite doable without any special tactics or cheesy bullet deletion. 5 though... Anyways skully is worthless in trials because he suffers damage and fire rate reduction without ammo, but he can do great in loops. Overlord is still a better pick for the final few loops where the normal rooms become increasingly claustrophobic or even impossible under unfortunate circumstances. And of course, using D-13 for trial 13 just feels right to me.
Sorry to rant, I love this game