PAYDAY 3

The first 3 primary weapons you'll unlock are the CAR-4 (starter gun), the Reinfeld 880 shotgun, and the SA A144 Marksman rifle. You'll likely be rocking the CAR-4 for at least the first dozen or so heists, as you work towards unlocking the following guns and earning money. If you're looking for the best gun to max right out of the gate, you can either stick with the CAR or buy the SA marksman rifle, which I believe to be the best gun in the game (or at least until level 60+) as it is able to 1-shot headshot most enemies.

Each heist you complete will award weapon xp, which awards the exact same amount to both your primary AND secondary. You receive no additional benefit for having a primary that's leveling up and a maxed out secondary, so you should try to always have 2 guns equipped that are NOT maxed out.

At first I thought I was going to have to PURCHASE every mod in order to get the achievement, but as it turns out you just have to UNLOCK the ability to purchase the mods, which is a godsend because guns often have high C-stack requirements for some later mods. Again, you just have to UNLOCK the ability to purchase the mods, without having to ACTUALLY purchase them. You can save your money!

Hope this helps!

EDIT: Levels required for the first 10 primary weapons to max the gun:
CAR-4 (AR) - 29
Reinfeld 880 (Shotgun) - 17
SA A144 (Marksman Rifle) - 24
FIK PC9 (SMG) - 24
Northwest B-9 (AR) - 27
Ziv Commando (SMG) - 17
KU-59 (AR) - 29
Mosconi 12 Classic (Shotgun) - 12
Reinfeld 900S (Sniper) - 14
SG Compact-7 (SMG) - 17