Curt makes a traditional hitch and a connector for the wiring:
http://www.curtmfg.com1991 - BMW 300 SERIES
SEDAN (inc xi, not M3) Install Time
30 Minutes
CLASS 1&2 HITCH
Product: 11514
Price Code: 55
Capacity Rating: 1.5
Instruction Sheet 11514
Fixed draw bar
T-CONNECTOR 1
3 wire system, requires converter
I don't know about towing a uhaul though.
I put a hitch on my scion Xb and its great for about 500 pounds but beyond that its really overworking the drivetrain. Plus an enclosed trailer uhaul behind an e30 is going to have a ton of wind load at highway speeds.
Figure 500 pounds for the trailer, 500+ pounds of stuff inside and the wind load and it'll be like towing a pretty hefty boat. From Chicago to Atlanta? Through the Blue Ridge mountains. I don't think so.
Also if you decide to do it, go over to the U-haul you plan to rent from and make sure they will rent to you with that set up. I took my wife's Explorer (one of the new ones, not the flip over variety) to get a utility trailer to haul my lawn mower to the shop and they wouldn't rent to me because it was an Explorer. No exceptions. Stupidest thing i ever heard. But they may question the BMW hitch set up since its not rated for towing.
Good luck.