Stay away from the Lumina Z34!!!!!
That 3.4 "Twin dual cam" engine is absolute POISON. The 2.8 and 3.1 found in the Z24's and Berettas have some issues as well (intake gaskets and head gaskets) but they're easy enough to work on. The Z34 is absolute garbage. Trash. ola.
If you're looking for a Ford equivalent, check out the 99+ Cougar. They can be bought cheap enough and work pretty good with the 2.5 and a 5-speed. Myself, if I were looking for a late 80's to early 90's 2-door econopoopster I'd try to find the "son of Thunderbird" 2-door, V6, 5-speed Tempaz. Far superior to any Cavalier or Beretta, rarer, and cooler looking to boot. Another possibility would be a Probe GT with the V6, though these can be expensive for parts due to their Mazda roots. I'd also think about a turbocharged LeBaron, which looks quite a bit like a 7/8ths scale 87-88 T-Bird.
If you wanna have fun, get a Beretta with bad rear shocks, pull on the e-brake, put it into reverse, and start pumping the gas pedal in a rythmic motion to get the rear end bouncing. You'll get the car standing up soon, and if you time your shots of the gas pedal right you'll have the back end bouncing right off the ground. Better yet, get a buddy with another one doing the same thing and you can race 'em backwards and bouncing across an empty parking lot. Always good for a laugh (don't ask me how I know this)...