Don't know if this is common knowledge or not and I've seen a few threads of people posting spots to skill up. Casters obviously don't hit very hard so they can enter any low-level instance and just auto attack for a long period of time.
Weapon skill up works like fishing, you just have to do it a set number of times for each point.
I started in RFC and off the first 3 mobs went from 0-350 unarmed. To level a weapon simply buy a level 1 weapon (minimum damage) and use that.
Again, sorry if it's a repost I don't have a search function yet.