Yay! First drives are always exciting! Yes, I strongly recommend to spend 20-30 min and tune your front and rear camber and toe (if your rear has adjustable toe), as well as centralize your steering, and adjust your servo horn, linkage, ect. to get even and central steering, you'll thank me after doing that! Just use an object like a piece of wood that's mostly square and level. It will run a lot better! Check out online for some camber/toe tuning guides, as for the steering, just set the servo to the center with the trim, adjust the servo saver so it's pointing straight up, 90 degrees from the chassis, then tune the steering linkage and get the wheels are straight as you can. Then go outside and trim the steering after running.
Keep in mind, that up front, when you adjust your toe, it will effect your camber too, and vice versa, so check several times that everything is good!
As for the veering....do the above, (your LHS can help with that) and then trim your steering. If while trimming you need to pull the steering trim significantly over to one side, stop and adjust your steering linkage. The goal is to get even or near even steering. A gauge is not neccesary, it's nice, but I tune my suspension with a pretty square/level wooden block, it's free and works well. So the steering play is in the ball/socket huh? In that case, try a new plastic socket, and also make sure the ball/socket isn't worn down with dirt or sand, and that the screws are snug.
Make sure the steering linkage isn't binding, and your servo could be on it's way out, and that crash may have helped. Tune your steering EPA (End Point Adjustment) too, don't have your servo trying to push the wheels farther when the steering is maxed out, you'll kill your servo.
Check this video out, by Amain Hobbies for EPA adjustment.
A smaller car is less stable due to a narrower track width (from one edge of the wheels to another, along the axle) and shorter wheelbase, but adjust the suspension first before making any calls. After that, try a compact "shortie" or stick pack, a compact, but slightly heavier battery might help in the way you want. Demolition derby huh...I find them as funny to watch as the next guy, but not when one of my cars is in it!


Rustler tough!