Big block and cheap usually don't go hand in hand. 68-72's had 396's and 454's in them. Finding a "cheap" original one would be a hard undertaking. You can buy a small block or 6cyl. car and install a big block, but that won't be to cheap either.
You are better off trying to find one with a blown motor or no motor (or the much desired 6-banger) and make the change-over.
As for cars that will fit the big-block without major modifications:
First Generations (59-60) came with cavernous engine compartments. The "Big-block" (396, 427, 454) did not exist at the time, but it is an easy swap.
Second (64-67), third (68-72) and fourth Generations (73-77) came with Big-blocks as an option, so they fit and parts are available. Motor-mounts, exhaust parts, springs, etc. are all available as over the counter items for these cars.
Fifth Generations (78-87) did not have the Big-block as an option and shoe-horning one into the engine bay has been done but would require major modifications.
If you are going on the cheap, try the swap-meets, eBay or want-ads for the car or the engine. Make sure you hear an engine run before you buy it. Sometimes you can find a decent body that needs an engine and put the two together. Here is an example of one of these cars:
I thought that I would reply to this post just cause it interested me so much. That was me 2-3 years ago. I was looking for a El Camino I didn't care anything about it I just knew I wanted one it wouldn't have mattered if it was a big block or small block. So here is what I did I currently have 2 El Caminos cause I didn't totally care. I got lucky 3 years ago I just happen to be searching the net and found a 1978 El Camino from South Dakota and the thing was in major mechanical repair. The body was great but the motor which was a 350 had the radiator problem and headgasket and all that fun stuff but the body was decent. Very little rust on the car however a year ago it slid into a bank of ice and did some damage and right after that the engine blew a rod not good. However do what I did go searching for anything and if you get something decent take it and as they say make it your own car. As with my 78 El Camino I just recently found another motor for it so that is going to be dropped in my car this coming week and the front clip will also so I am excited. But look towards a newer one but if a old one comes up jump on it. Also make the search for one part of the adventure of fixing it up. Make it father son day searching for cars.
before you buy one always look under the car at the floor pans. this is a weak spot on most of these cars. as far as installing a bigblock. it is a very easy task if the elk came with a v8 then your supports will work as is. but if you run tall valve covers you will have to remove the air condictioner box,or cut the valve cover corner off the passanger side . again this is no problem. good luck