If a land has more than one basic land type, it can be chosen more than once.

Players can't take actions in between the time you choose the lands and the time you destroy them. Notably, they can't activate mana abilities of those lands.

Sundering Titan's ability isn't targeted. When it resolves, Sundering Titan's controller must choose one land for each basic land type (Plains, Island, Swamp, Mountain, and Forest), and then they are destroyed simultaneously.

If one of the basic land types isn't present, it isn't chosen. If the only land of a certain type is one you control, you must choose it.