On Panzerfausts: Is it really worth it to give a few tools to a rookie who may not even know what to do with them, at the cost of reducing the options of everyone else? I don't think so. I remember Dioxine saying he intended people to make multiple playthroughs and learn things and making sure you have the tools to deal with all kinds of bad guys is a lesson one should learn early (as you did). It would be much more frustrating to get by on luck only to fail later, after you have invested a lot more time into your game.
Regarding starting game, that sounds about right, for starting priorities. I try to get a full crew (and some more to step up and replace wounded gals) asap. I however don't buy RPGs and other ranged explosives, the gals' aim is too bad to rely on that. They get the job done by throwing explosives, firing bombs, setting them on fire, or when all of that fails, hitting things with a hammer. Until you can make your own ammo for RPG, it is just too expensive for the unreliable effect.
I also focus on researching armor techs unless I feel I am really falling behind weapons wise (which usually isn't a problem at the beginning as the melee weapons + black powder bombs get the job done). Having good armor is key to getting gals to survive, which is means they are racking up experience instead of dying. If you can keep your gals for a long time (by being "careful" with team tactics and dog scouts) you can get really monstrous gals. I have had a few 60+ reactions, 100+ firing accuracy ones, high Str and TUs gals who could be depended on to do just about anything.