What card sleeves should I get for Cards Against Humanity?
None, but I am betting this was a trick question. The cards dimensions are fairly close to the standard dimensions of a Magic: the Gathering card. The cheapest card sleeves you could buy are the aptly named penny sleeves. These sleeves will run you on average $0.01 US. Since Cards Against Humanity runs 550 cards in the base set, you would be spending $5.50 to sleeve the cards, slightly over 20% the cost of buying a complete replacement of the entire game. I suppose if you buy online, and sufficient quantity, you might be able to reduce the cost of the sleeves by 20%-30%.

Sleeving will increase the thickness, so it will not fit in the original box. There are other issues with sleeving. Sleeves of any sort make shuffling more difficult. Penny sleeves are also notoriously slippery because they don't have textured backs (Like Dragon Shield or other high quality sleeves). High quality sleeves would cost you more than the original game itself to sleeve. Games are meant to be played, and this game wouldn't suffer much from having marked cards. As an Apples-to-Apples clone, the only danger of marked cards is that the judge might know which card you or another player through in the pot. This problem can be eliminated by having the judge close his eyes, look away, and having someone else shuffle the cards before giving them to the judge (we usually do this anyway to prevent the top card being the card from the person who decided last).

I would recommend against sleeving.