since you're driving, you have the luxury of taking some things. i would pack the car to the brim, as money will be tight.
i think it would be good to take a pair of curtains and possibly even the curtain rail and clips along. you'll probably need to hang curtains in your bedroom immediately. i would take a lamp too along with a couple of lightbulbs that you probably have in a drawer at home. i've moved into places that don't have one lighbulb in them before.
and yes, take some tools, as you'll need those right away and they are expensive.
i'd throw a power strip, a flashlight, scissors, and a good kitchen knife. i would also take my favorite spices, as they are expensive to recollect and your AH probably won't use them.
small rugs are handy too, as if you're stuff isn't there yet, you can pile them up on the floor and sleep ontop of them.