In terms of speed they aren't that fast compared to most cars today, back then when it came out it had decent speed but nothing overwhelming. It's about a 130hp car. If your looking for a cool looking crusing car this is a great car, if your looking for a street racer this is not the car for you. The price generally ranges from $10k - $25k for a used one and I think it's up to $40k for a refirbished one from DMCH. I wouldn't recommend a low end Delorean because it will cost more in the end to get it in good shape. It's best to buy one that is in good working order that hasn't been sitting for more than a couple months. Never buy one that says it's been sitting for 5-10 years unless you have money to burn. Deloreans don't like to sit for long periods of time without being driven. You can generally find one that runs ok, and is in fair to good shape for about $15k.
It depends where you live to how difficult it is to find a Delorean. If you live in Florida, Texas, New York, California, or Arizona it shouldn't be that hard because thats where the majority of Deloreans are usually found. If you live overseas then it is much harder and much more expensive. Try Hemmings.com, Cars.com, and autotrader.com to look for ones near you. I wouldn't recommend Ebay, their seems to be a lot of Delorean selling scams on there.
In terms of budget, it is a car that is almost 25 years old, so things do go out now and then, but that also depends on how well the previous owner took care of it, and how many updates he had done on it.
They are easy to clean despite what most people say. I hardly ever wet it down. I just spray stainless steal cleaner on it and wipe it off and get a great shine that when the sun hits it just right you get a cool prism of colors.
One last thing, I see you mention GM. GM didn't have anything to do with making them.