Classes don't specialize in weapon types any more, and for the most part you don't need to just use every item in a set nowadays. Most of the sets you end up making ideally only use 1/2 pieces of a set to use the newer trophies.

Is it 100% necessary to have professions in this game?

No.

what exactly should I be working on and how do I start making some Kamas to avoid out leveling any sort of affordable gear?

You want to focus on things that'll give you a bunch of materials to sell, and sources of raw kamas. The Almanax is a daily quest you can do on every character you own, where you retrieve some sort of resource and bring it to the Almanax temple at -4,-24 and depending on the resource you could make a few hundred to tens of thousands of kamas per character per day. I believe the only requirement to do this is level 20. Here is a website that tells you what the required item is every day: https://www.krosmoz.com/en/almanax

In addition, you should do pretty much every monster and dungeon achievement (press u to open the achievement interface) you can and just selling any resources you get while doing those.