One piece of advice..... Sidewall construction snowboards hold up a lot better to the abuse that is kite snowboarding than cap construction boards.
Side wall is exactly that. The top sheet comes to an end and you can see it in cross section from the side with another material making up the side wall down to the metal of the edge. There will be a sharp corner from top sheet to side wall. These are side wall boards:
Cap construction is when the top sheet is moulded down from the top of the board down the side to the metal edge. There will be a rounded corner from top sheet down the side. These are cap construction:
Hope this helps.
As for board shape and riding style. Generally go for a type of board that closely resembles the type of riding you will be doing with your kite. Deep powder, get a nice wide powder board. Wind swept lakes, get a board designed for groomed hills. Wanna hit kickers and jib off stuff, get a park board. Thing is, anyone who knows how they wanna ride, already knows all this stuff!
If your new to snow kiting, your safe in knowing that in general most middle of the road designs work well as they allow for a fairly balanced binding placement on the board. Anything too downhill oriented will have a lot of offset to the inserts and have a definite bias in direction. If its your first snowboard for kiting, don't spend a ton of cash. You are far more likely to hit rocks, earth and plenty of hard ice with a kite. There are a few people who like having a board with no side cut for the times there is ice but little snow. They are not my choice, and I would rather wait for snow, but they work in those conditions.