Old rwd Volvo. 240, 740.
These are very cheap (less than a Fox body), have plenty of engine room, are well supported in the aftermarket and just easy to convert to LS, all parts are available to do this swap from many vendors. I'm talking about `94 to`98 Mustangs. The Pick and Pull near me always have 8-12 of these at all times. They are a Fox Body in a way, only more aerodynamic (see windshield angle) a much nicer interior. You asked.
I'm looking at doing a 1983-1985 Monte Carlo swap. Couple grand for a really nice body and decent looking car. There's been a few done, but seems like almost everybody is doing a Mustang.
I'm planning a 5.3 & 4L60E swap in a 1966 ford bronco that I'm restoring.
I'm with Norm, mid 80s G body (Monte, Regal, Cutlass). Good looking, RWD, cheap, no emissions (here anyway), and kinda practical (4 seats).
GM B,D,G-body relatively inexpensive and can easily be dual purpose, cruiser/street, track on the cheap and many parts in the junk yard.
I just bought myself a 2001 bmw e46 coupe for my ls swap. Running and driving for $1300!!! Sold the engine/tranny for $1k. So the car was $300. Plus I'm getting rid of all the interior and wiring and putting a cage but theyre guys out there racing with 2500-2900lb weight , without the ls which I think is lighter than the factory I-6.
I've seen a lot of e46 coupes going for 1500-2500 so that might be a good possibility for you.
It goes on....2nd gen RX7, bought mine for $400. Sold the motor with a bad apex seal and transmission for $350 and the RX7 PCM for $75. Actually made money on the deal lol. And the swap is relatively easy. No cutting or welding involved.