Easy and difficult
By the rules, you could use literally anything for either model, until the official plastic battlewagon comes out. Technically, you could field a classic ork trukk (about the size of a wallet) as a battlewagon. There's nothing saying you can't. Of course, I think your average player is going to call shenanigans on that one.
Looted wagons are easy. Any 40k vehicle will work, although it probably should have wheels. I use a rhino as a looted vehicle, as it's the cheapest vehicle you can buy. You could also use a trukk if you like (although that might get confusing if you're using other trukks in the list). For looted wagons, I'd look on ebay for bargains, since it doesn't really matter if it's a little damaged. In fact, that's probably better.
Battlewagons are trickier, and no matter what, unless you use a Land Raider, at least some people are going to complain. I say let them complain. They're too expensive. Instead, I used a rhino hull, several plates & wheels I had left over from a trukk set, and a large plate glued on front that I got in a lot of random bits, that's actually the back of a baneblade. I don't see anything wrong with something like this, but the best compromise between cost and look is a Leman Russ. It has the same armor of a battlewagon and it looks nice. Some people will probably complain that it can't realistically hold 20 people, and my response is that a rhino can't realistically hold 10. The vehicles in 40k are representational. In reality, they'd all be bigger, considering they wouldn't be hollow inside. The engine and equipment would have to fit along with them.
Well, I've ranted on a bit now, but for a looted wagon I'd use whatever's convenient. Either look for a cheap rhino, or if you got some extra bits, I'd find a basic rhino hull (they're relatively cheap on ebay) and then attach a bunch of stuff. The weirder it looks, the better.
For the battlewagon, I'd use a Leman Russ, with extras attached if you like. I wouldn't use a Land Raider though. Again, they're too expensive. I'd stop using battlewagons first.