I don't really want to play campaign and puzzle mode, but I would like to be able to use the other classes. Is there anyway I can do this?

No.

If you want 1 of each class then you'll need 240 credits.

You also earn credits for taking part in ranked games, so if you don't want to play the single player modes you can unlock them that way as well.

A quick way to get them is to complete the first 5 Sewer puzzles and then the first Beach puzzle, which gets you exactly enough to buy your first Scientist, Scout and Heavy.

Thanks for your help