Beginner

C kite: Older design, not quite as efficient a wing as bow kites and does not provide as much wind range, but very predictable and 'grunty'. Distinguishable by squared off wingtips.
Bow kite: Newer design principle with swept back wingtips and the leading edge supported by a bridle. Has more wind range and more depower than a C kite, but this isn't always what you want.

Bow kites are generally regarded as easier to learn on and better for beginners.

Size depends on your weight, the size and type of board you ride (I would recommend learning on a twintip), and the wind strength where you will kite most.

The best thing you can do is to get professional lessons, and your instructor should be able to fill you in on the finer details.

Oh, and use the search function here. All of this has been covered in detail many times.