Yeah I ended up just resetting after I lost two of my bases. I think the biggest problem in the first play through was diddling around with all the weapon requisition techs that I wasn't even going to end up using. I did have the kitsune and the interceptor and I believe my best weapon was the black-ops magnum/regular magnum depending on money I want to spend. They carried my past the humanish enemies and some of the weaker enemies after that, but fighting the underground aliens was hard with just magnums and grenades as the mainstay weapon.
Fighting with what are basically just handguns is a problem. You should look at it like the 'real' military and have combined arms, depending on the size of your squad. With a Dragonfly squad (8 troopers) I have 2 with rifles (the best available, preferably Smartrifles or UAC rifles until lasers come along), 4 with P90s or UAC SMGS for CQB inside bases/UFO's, and of those 1 or 2 have grenade launchers to take out stubborn or large enemies. The other 2 have an MG (Blackops LMG) and a cannon, preferably light- or auto-cannon, which are useful if the enemies bunch-up. The amount of weapons the squad carries scales-up with size of squad, and with an Osprey (and larger craft) I make sure 1 or 2 troops have sniper-rifles for long-distance and also 1 or 2 have heavy anti-tank weapons for those really tough missions (useful to take down walls).
Early weapons don't need to be standardized, and I like to give my bases the 'local' guns, like M16s in the USA and AKs in Eastern Europe. Once you get the better stuff like Blackops and UAC you should make them standard in all bases if possible.
Another tip is don't research acquisition of weapons you know you're not going to use and spend the time of getting better armor/vehicles/weapons. Also research captured enemies and creatures asap as they can give better research topics and info on weapons and things. Research any science building that comes up as you can't research some topics without the newer ones, and they add extra research spaces too.
I really must sit-down and write an essay on my own playstyle sometime as there's so much in Xcomfiles!
Buying and opening loot boxes when they're available (reinforced weapons boxes are good) can sometimes give you early use of high-end weapons. I once got an early Hydra-laser that way, but I had to be spare with the ammo!