What kind of paper can I use for a game card?
If you are looking to prototype a game there are really three options, you'll want to weigh Expense vs Effort vs Polish. Obviously if you are just playtesting (especially early in the process) Polish is not important, and keep expense and effort low will probably be helpful if you're going to be iterating your design a bunch!

There are three main options:

Print on heavy weight cardstock

Pros: fairly cheap, very low effort

Cons: Not very polished, cards will exhibit wear fairly quickly.

Print on paper and sleeve w/ CCGs for stiffness 

Pros: Sleeves are probably the expensive bit, as it's not too hard to find someone who'll hook you up with junk commons from a Collectible Card Game like Magic. You can print on regular paper, and if just a few cards need changing it's quick and easy. Great for iterative design

Cons: Not everyone has access to junk cards to use as backing. Not polished, especially for final version.

Print on Demand Example: Drive Thru Cards

Pros: Assuming you've got good art skills can look professional/polished.

Cons: Not cheap, also not cost effective except as a vanity run/final playtest/review copies.