Well I'm assuming the 737 -300 (and not the B737-200), flown on both classic and NG, the classic has a few things which you cannot program into the FMC, which the NG can (you'll basically have to do it manually). Also the weather radar controls are on the side instead of on the MCP in the classic. Though the classic is better to control, but look out for those landings, as you'll feel more on the landing in a classic than on an NG, well thats from previous experience.
Well eaglejet do a line training program with TR, that would work out cheaper than other institutes probably, though I heard there is a long wait. If you do your TR in london with one of there partners, then do the line training with eaglejet, you'll get some kind of discount, think it is a few thousand pounds, but you should ask them to confirm that.
Happy Landings...