Well, have you tried going to the market and buying the blueprint for a rifle yet?
Also, you can power up your weapons with various mods, but some are more important than others. For primary weapons, you want Serration. For pistols you want Hornet Strike, and Melee needs Pressure Point.
Those are things you should look out for, as they are possibly the most useful things in the game.
But yeah, the Market is where you’re gonna get a lot of weapons from. Buy the blueprints with credits, and then craft them in your Foundry.
If you have not joined a clan, I recommend finding one with rules that suit you. I joined a soloer’s clan a while back and it has made me a lot of friends through this game. Clans are really damn useful. If you’re not the most active person, then you’ll want a more lax clan.
But yeah, for now, just explore the options you have, unlock some planets, and level your gear when you can.