If you are diving in tropical waters, a lycra suit might do – it will protect you from stingers while not overheating you.
In any cooler water, a neoprene suit will actually help keep you warm as your body loses heat faster in water than in air.
Neoprene is a spongy material made from foamed rubber. It is quite sturdy while maintaining flexibility over a wide temperature range. The thickness of your wetsuit will depend on the climate you want to primarily dive in.
In general, a 1-3mm thick wetsuit works great in 25-29 degrees of water.
For temperatures between 22 and 25 degrees, a 5-7mm wetsuit is most adequate.
If you are diving in 20-22 degree water, a wetsuit of 8-9mm thickness is recommended. In that scenario, you might also want to look at getting a semi-dry scuba suit.
For commercial diving, closed cell neoprene suits such as the Fisterra are best. Closed cell neoprene is less exposed than open cell, and therefore does not compress as much.