First off, I wouldn't be claiming the Delorian. It looks okay, but they had MASSIVE problems. Personally if i was going to get a car from a movie, I'd go for the Sterling(also called Nova) kit car that was used in Death Race 2000.
The Delorian had overheating problems. The new ones have fixed that. They had difficulty REACHING 88MPH as they were underpowered. The new ones have been seen with V8's and more commonly high output V6's. The steering was... at best... marginal.
I had an opportunity to buy an original for I think $6k a few years ago. I was somewhat underwhelmed.
The new ones will set you back about $55k(US). Which if you're keeping track of these things, would mean you could get a NEW CAMARO SS and still have enough to buy a used Delorian.