go, but with more thought
Welcome to the RTA Forum!
I'm certainly not going to say that you shouldn't go, but I am going to tell you that I you need to put some serious thought into how you are going about doing this trip.
I would have some serious doubts about the roadworthyness of any van you'll be able to find for under $1000. Realistically, you're going to be looking at a van that is probably going to be 15 years old, with high miles, and probably in pretty questionably shape. Its certainly going to be at high risk of breaking down, which when you'll be thousands of miles from home and often in some pretty open areas that will be long distances between towns.
As far as what you'll need to have checked by a mechanic, the answer is everything. There are thousands of parts in a car, and there is simply a matter than any vehicle of that age and price range are going to have things that are going to wear out and break. Even a inspection by a great mechanic might not catch everything, but it should give you a good idea of what things are at highest risk for being problems. In any case, you'll need to have a significant reserve fund to pay for towing, repairs, and in the worst case, another mode of transport home.
Financially, you should also remember, that even with a cheap van, you're going to have to spend about $150 for title and registration in Wisconsin. Its the same price if you spend $500 for a van or $50,000.
I will also remind you that even though you are heading to California, you'll likely see a lot of cold nights during your trip. A van doesn't provide much more protection from the elements than a tent, so you need to think of this in terms of winter camping, and have the appropriate cold weather gear. Sleeping with the van running for heat would put you at risk for death by carbon monoxide poisioning.
It rarely makes financial sense to purchase a car just for one trip. If you or your friend already have a car, then it probably will make more sense to just use that. Otherwise, I'd look at finding something that will be practical not just for your trip, but that you'll also be able to use once your trip is completed.