I really want to make game card that's similar to Monopoly cards or the like.
What kind of paper should I use for the cards?
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.
How about going ahead and printing on 110lb card stock, but putting the cards in sleeves? Seems like that would work, plus they'll look good. You could also consider printing them on matte or glossy photo paper for a finer finish. As for the backs, I've accidentally printed on the wrong side of photo paper before, and not only did it print very good, it also gave the feel & appearance of textured cards.