Well I "borrow" the laminator at my office
I know that some copy shops like Kinko's and OfficeMax will laminate things if you don't have a laminator already. They are kind of expensive to buy if you don't have a lot of uses for it. (Although I never seem to have trouble finding things I want to laminate.)
I guess my only recommendation would be to have them laminated with a machine that uses high heat. There is this one (low heat) type of laminating that just fuses the two sheets of laminating plastic to each other around the perimiter of the thing you're laminating. That wouldn't really work if you were going to then cut the cards up (the plastic would just peel off the card.) The higher heat stuff actually kind of melts to the object you're laminating so then you can cut it up or trim it really close with out it peeling. Does that make sense? (It's kind of a hard thing to describe.) I think most of the laminating machines these days are the high heat variety.
The nice thing with using cards is that you should have some extra images to test the laminating with. (Laminating is always scary when it's a one-of-a-kind piece of art or something.)
You could also try clear plastic packing tape... it doesn't come that wide and sometimes it gets kind of gummy on the (supposedly) non-sticky side but it's cheap so you could play with that.