You can get a decent sawz-all (reciprocating saw) for under $50. With the right blade you can use it on anything, even to cut firewood, so why rent one? You'll need plenty blades -- I cut up a whole wreck like the wagon in my avatar, I think I used 8-10 blades. The big unbraced panels (like the roof) will be the hardest to cut. You can use an abrasive blade on a HD skillsaw too. Abrasive blades are a bit expensive and don't last long -- take you time if you go that route and don't force the blade through, that REALLY eats them up!
I've seen a car cut and hung on a wall similar to what you're doing, but it was cut roughly along the fender/hood line down the side of the car. There was maybe a couple inches of hood tacked in, just enough that the whole side of the car could be used. The doors would open and close, but not enough room to climb in! No "frame" -- wheels were bolted directly to the wall. Something like that would be a better bar ornament (I saw it in some car museum somewhere...).