Since you're on a budget, I'm going to go the route we went for a couple years. We didn't have access to a space where we could set up permanent bench tools, so here's a list of essential hand tools.
- Wire Strippers
- Wire Cutters
- Crimpers
- Pliers
- Socket Wrench Set
- Allen key set
- Drill/Impact Driver
- Drill bit/hex sets for the drill/impact driver
- Jigsaw
- Angle Grinder
I'm probably missing a few, but these are what I can think of off the top of my head.
It's not a tool, but make sure to have plenty of hardware like bolts/nuts/etc.