I’d say either regular paper + 10mm lamination, or 12pt matte paper (what people use for lower-end business cards). Regular 65lb or 110lb cardstock is probably not going to cut it for playing cards.
If you’re going to laminate, remember to cut out the cards first and then laminate (and cut out again once it’s laminated). That way each card will be fully sealed around all edges and waterproof.