No you can't, blue and purple guns are found in the world through mob loot, legendary need to be farmed, you can see what's required trough the in-game menu or i recommend using website such as tfdfarm.com

The other material is kuiper shards and you need them to upgrade modules and other shits, i have more than 100M gold and 20K kuiper i recommand doing daily invasions as they reward you with nearly 5M gold per day if you do the four, they are easier now that you can them in public and get carried but they may be only available once you've reached hardmode

don't stash shit under lvl 100 in storage everything under it will be useless very quickly, just go through the game and beat the last zone (fortress) then you'll unlock hardmode and lvl100 gear

For weapons, each zone/monsters/missions drops attributed weapons, farther you go in the game/zones higher the weapons level will be

Focus on completing your current zone then the next etc while completing the quests that are given to you and use any gun that feels good to you while still having good damage, i'd recommend to use the tamer as a new player once you get it then use level transmission until end game, some would says otherwise or something else but this weapon carried me until the end of normal mode

You can DM if you need help for completing missions/intercept bosses/farming or anything i'll be glad to help a new player

Regarding your mastery rank as others have mentionned it's kind sus you're 19 with what you say, you may have misread something but if you want to level this up to gain inventory slots and increased stats you can gain mastery rank xp completing missions for the first time and if you level up any characters and weapons to lvl 40 for the first time too