Early game: Whatever is on hand to get me out of a jam.
Late early game: Pneumatic bolt driver. No contest. This bad boy opens up the world for you. I still use it in late game lab dives, too.
Mid-game raiding: Either an RM99 or RM103A. Very powerful, very accurate, the ammo isn’t all that rare, and handmade versions of the ammo can be crafted in (nearly) unlimited quantities. When you are melee-ing a town and just want something in a holster to deal with shockers, brutes, and hulks, one of these is what you want.
Late game: I like the RM88 battle rifle, although it isn’t a horrible idea to also keep a Barrett or a rail rifle around for roadblock clearing duty.
Honorable mention: L2037 Backup (if you can’t get a big Rivtech pistol,) FN Five-Seven or UCP as an ankle holster backup, and, of course, the mini-speargun. For training.