So I'm extraordinarily picky about socks and have mastered which pairs to wear in WDW.
As others have said, absolutely no cotton. Cotton holds onto moisture and will keep it up close to your body. Serious hikers won't wear any cotton clothing. Touring WDW can be treated like a serious hike
Merino wools socks are 100% the way to go. Thin socks that aren't heavy hiking or winter socks will be closer to around 50% merino wool. Don't be tricked by socks that are only a few percent (5-20%) merino.
Probably the best brands are Smart Wool, Icebreaker, and Darn Tough. Smart Wool has a line called 'phd' that I think are the best. These are the lighter thinner wool blend socks. They aren't itchy at all. Pairs of merino wool socks will run around $7-$25 for a single pair. They are way more expensive than cotton socks but they are 100% worth it. The PhD line SmartWool socks have no show, ankle, quarter crew socks that are all good for the hot Florida weather.
You can save a good amount of money by buying SmartWool socks at Sierra Trading Post (its a website, google it, there are always 20-30% off coupons available, sign up for the mailing list). If you have an EMS near you they have a huge selection of SmartWool as well.
Spend the extra money on some SmartWool socks and you'll never go back to swampy cotton socks again!
EDIT: Just going to add, you can find Wigwam brand wool socks at Target but they are usually a lower percentage of wool and are pretty heavy. You'll be surprised at how thin and comfortable the SmartWool PhD socks are. Don't let the heavy wool socks turn you off.