Your background in boards sports will come in very handy when you get to the stage of riding on your board, but unfortunately has little to nothing to do with learning to fly a kite. It's a bit like combining two sports: kite flying and wakeboarding/surfing
Everyone reacts differently when comes the time to learn to control a kite. I've had many very experienced surfers who were simply not ''natural'' with kite flying and needed a few extra hours of lessons just to get decent kite control and get used to the power of the kite.
Your first lesson is the most important and at the end of it your instructor should be able to assess your skills and recommend the best course of action depending on your own learning pace and recommend a certain amount of lessons or practice time you will likely need.
My best advice is to try and pace yourself: don't try to take shortcuts and beware of people telling you things like ''you will be up and riding in just 4 hours''.
Shallow water areas are very easy to learn in where you can feel safe and can progress to the board in 3-4 hours with an instructor next to you. Unfortunately, those over-simplified teaching methods in those environments do little to prepare you to deep water kiting (most common locations) and the one as a surfer where you'll likely spend the most time...
These days, lessons are becoming more based on delivering a fast paced thrilling experience with constant hands-on assistance rather than genuinely preparing you to become independent and safe when practicing on your own. The difference between the two is huge and mostly noticeable in deep waters when beginners get in trouble or fail to recover their boards (just look at the lost and found section in the middle of the season

)
Flying a 2-line trainer kite can help, but I wouldn't recommend ''flying the $hit out of it'' without supervision or exercises to follow. Although it can be a lot of fun, this usually leads to learning dangerous flying habits that have little to do with your first experience of flying an inflatable kite and can become difficult to break during your lessons. A more efficient way to prepare for your lessons is to get your hands on the beginner progression DVD and read the forum, watch learning videos online, etc.
As per the board, I would recommend to even the most experienced and skilled surfer to at least learn on a twin tip until competent going upwind and doing transitions before going onto a surfboard, even if it has straps.
Hope this helps,
Christian