I never really saw a reason to use a weapon that isn't your type unless you are forced to as most characters bonus' relate directly to their weapon "expertise". By forced to I mean, Purna start of the game usually doesn't have access to a gun so she is "forced" to use other weapon types.
In Riptide you gain weapon experience by getting kills with the weapon which in turn gives you bonuses with that weapon type. Each character should also have durability skills that either relate to their weapon type (blade, blunt) or the handed-ness of the weapon (two-handed or one-handed).
In terms of selling weapons I keep about 4 weapons specifically for my character to use (more if you find yourself running out before you can find a repair table) and the rest of the slots are kept "for sale" for selling weapons, i pick up everything - when my inventory is full i start discarding the lowest price weapons, and replenish with higher priced weapons. NEVER tossing any of my items that are "in-use", ie. the ones your character is using to fight.
When you are looking for weapons to keep for your character, consider the type (each weapon has an icon in your inventory telling you the type), if it matches the type you want to roll with and it's damage is better than any in your current rotation consider keeping it. Xian's main method of getting through fights is just by slicing and dicing, characters like Sam B and John need to worry about force (knock-back).
The higher the tier the weapon the more it will cost you to upgrade and to repair, the higher you upgrade the weapon the more it will cost to repair. Look for really good green weapons. The tiers go something like white, green, blue, purple, orange/yellow (best). Green weapons can do just as good damage as blue and purple - they are also cost effective when repairing and upgrading - which really won't be a concern mid to late game if you are continually picking up and selling items.
Don't upgrade everything you find right away, I found this the best method of conserving money, I would keep weapons I found and only occasionally I would upgrade them or mod them until I got to level 40-50 when I really started pumping money into weapons. You level up pretty fast so you will always be finding new and better weapons early to mid game.
As to what to keep in your active slots, if you are playing alone and you open up the actual inventory menu the game will pause, the quick menu won't pause. I tend to keep a weapon for every situation. My first character was the melee guy so I kept two melee/hand to hand weapons, a harpoon gun (for ranged, suiciders etc) and then one slot for a grenade or thrown of some sort. As I gained more active inventory slots I started keeping one or two melee weapons, one thrown (explosive) and the rest were guns as they really seem to be the best option in Riptide (whereas they weren't in the original).
Also guns do not have repair costs.
Hope this helps!