Well, at the start you do need to rush the firing and reactions training of a couple of gals so they can serve as pilots. But other than that, I find that maxing out melee first works better in the early game. At least if you're an expert at doing night missions. I should note that certain early game enemies, like Highwaymen or Church Priests have enough armor and stun resist to take a substantial amount of Domestic Shotgun stun slugs, so they're easy to max firing training on. And of course, Necropirates are just great for training overall.
Heh, there's one training strategy that involves stacking 11 stunned enemies on one tile, and hitting them with Grenade Launcher /Smoke slug, and Fire Extinguisher, to max out your firing and throwing, all while doing 0 hp damage. The problem is, /Smoke slugs aren't available early game and fire extinguisher isn't particularly portable.