Hey Sutton,
You can use any kite type it just depends on what your after.
A 4 line kite with handles will give you good control and you can use either brake individually. Look for one thats not too fast and sits well at the edge of the window. HQ Beamer, PKD Buster and Peter Lynn Hornet are all good options.
If you go with a foil on a bar you wont have the same control over the brakes but they can be more suited to freestyle as you don't have 2 handles to worry about. HQ Scout and Peter Lynn Twister are good options.
Your other option is a de-power foil on a bar. These will give you a larger wind range and the ability to ride the gusts better. They will also allow bigger jumps if you get the technique right.
They are more expensive but cover twice the wind range of a fixed bridle kite. Some can be used for kitesurfing as well. Look for HQ Apex, Montana or Neo. Peter Lynn Arc. Flysurfer.
The main thing you will be looking at the beach for is hard pack sand. If it is soft in any way you wont be able to landboard. Don't worry about going for 9" tyres as there is no real advantage 8" will be fine.
When looking for a freestyle board the shorter ones are better but longer boards are better at speed. Weight is a big factor when comparing boards.