Most people wear something under their wetsuit to help with getting your wetsuit on easier. The other reason for wearing something under your wetsuits is that the extra layers can help keep your body warmer. Instead of wearing a thicker wetsuit that will restrict your movement it allows you to wear a thinner suit that will give you more flexibility. You can wear a short sleeve top or bottom to help keep your core warmer. The other thing to think about is the air temperature/ wind on your way to the dive site. If you have to worry about the air temp/ wind when you are traveling to the dive site, a linebacker jacket (the kind football players wear on the sidelines) is good to have as you can take it off before the dive and put it on when you are done. For colder temperatures, adding layers underneath the suit is definitely the way to go. You have several options to choose from. If you already have a thinner wetsuit that you usually use for warmer environments a 1mm rash guard, or any other type of garment that’ll provide you with the added warmth around your chest will help.
When you have to worry about the wind most surf wetsuit or wetsuits that are glossy like surf suits, are designed to stop the wind. That all suit surf suits are not great for diving as most are not made from a material (yes surfing is different then diving) that is designed to be used under water for long periods. Some people go nude under their wetsuits. After wearing a wetsuit for an extended period of time, this can be painful, due to the constant rubbing against their skin it begins to chafe. Normally the neck, armpits, behind the knees, and the crotch are the first to go. You can apply anti-chafing gel/ Vaseline to help with this on long dives. You can also wear a dive skin or bike shorts this will help with getting your suit on and off also.
Whatever you decide to wear keep in mind the water/ air temperature, duration of the dive and what you will be doing. That should put you at a good starting point.