Good question. It depends, there are a few reasons why you would wear something under your wetsuit. If you want to wear something because you want to be warmer, because your wetsuit is too thin for certain water temperature then get a thin top or a thermal rashguard. You can also get neoprene shorts. These will not influence your paddling that much and will add to the overall warmth. Wearing a thick top under your wetsuit will make moving your arms harder.
If you are just wondering what people normally wear under their wetsuits? Nothing! If you know you will have to change in a public place, if you feel that hiding behind the towel is clumsy or if you are renting a wetsuit and don’t want to be naked in it – then put a bathing suit under it. Use a normal bathing suit like speedos (dickstickers, nuthuggers… :)). Do not wear boardshort as they will wrinkle under the neoprene and feel uncomfortable. If you are a girl you will also want to wear a bikini top or a sports bra.
Wetsuit can also cause rash or wetsuit chaffing. Rash can appear in areas of your body where there is a lot of movement and your skin constantly rubs against the neoprene. The usual places are your neck, your armpits, behind the knees, your ballsack… with neck and armpits being the most common. To prevent this – wear a rashguard under your wetsuit.