I think surfing looks like a lot of fun but I would be a little worried about sharks.
Yes, i like it surfing too, native peoples of the Pacific, for instance, surfed waves on alaia, paipo, and other such craft
Is it difficult to surf, does it require a lot of balance or skill?
Well surfers can also utilize artificial waves such as those from boat wakes, i think when you learn it its like learning to ride a bike, you cant forget it
I wonder if it is similar to water skiing? 
Its a water sport in which an individual is pulled behind a boat, so i think that its a department of surfing :D, and can still be called that way :D
Is the equipment like surfboards complicated or expensive?
They need to be relatively light, but strong enough to support an individual standing on them, i think they are, best ones are handmade i think, 
Handmade would explain why they cost so much that is a lot of time and labor.
You should first try some other types of surfing like knee boarding, surf matting (riding inflatable mats), and using foils, when you learn you can do real surfing :D
Is it similar to paddle boarding? I was fairly decent at that on vacation.