In GTA 5 Online you only start off with your free pistol from Lamar, but unlike Grand Theft Auto Five story mode, it can be quite difficult to acquire new weapons and ammo. Luckily there are a few ways around that.
One of the first things I noticed playing GTA 5 Online is that some missions gives weapons you cannot find in game. When you do your first Death Match you may notice you can find weapons on the map. Any weapons you find in missions you will be able to keep until killed, or possibly logging out (unconfirmed).
However, I noticed the best way to get weapons that are unavailable to your rank on GTA 5 Online. Join a survival mode, which you may need someone higher rank to queue at first. When I did my first survival missions, running a few times, I left with a grenade launcher, a couple types of all guns, and even more ammo. Now be warned, if you run out of bullets you may lose your weapon. Luckily, some weapons use the same bullets as higher level weapons, making it possible to keep ammo stocked.
So if you highly geared out with weapons, be sure not to die if possibly. I know, easier said than done. But it is easier armed to the teeth. Also be sparing in the player map of using the weapons, since they are limited. But you can always go back for more.