Surfing is a breeze if you're just beginning. If you're that fit and have snowboarding and swimming experience, you should look like you've been doing it for a while first time. I wouldn't worry at all. I am pretty unfit and clumsy and I got up on the board first time I went surfing. Seriously, it's a total rush and I bet you'll love it!
Tips - make sure you don't get up too soon otherwise you won't catch the wave. When you feel it powering you forward, that's when you get up.
don't stand too straight when you do get up, crouch and use your arms to point you in the direction you want to go.
to avoid taking a nose dive on a steep wave, press your feet down on the back of the board to weigh it down as you first come down the wave (this works even when you're still lying down).
when going over the edge of a wave as you paddle out, to avoid crashing down, press your hands down on the board for a smoother 'landing'.
if the current is pulling you, swim perpendicularly to it.
paddling - cup your hands and keep your fingers together, that way you will move forward at a better pace.
practice turning (each arm paddling in a different direction - switch arn directions for turning left or right). The faster you can turn, the more waves you'll be fast enough to catch.
if a huge wave is coming towards you, and you're panicked, either paddle forward powerfully to get over it, or throw your board back and dive into the wave (this last bit should only be done if there is no-one behind you that might get hit, and you have no other choice). If you have a small, lighter board, get the instructor to teach you to duck dive, it's so useful.
Try and always be aware of people around you. Never sit in the water behind someone - you are blocking their path and putting yourself in danger.
Hope you come back and tell us how it went