Kitesurfing first started using directional boards. Later, bi-directional twin tip boards were developed and became the predominant board type.  The good news is, you can have one or more of each.  Both have their advantages in different conditions.
Board types:
* Twin-tip: the most common board. Used for free-ride, wake-style, cruising.  Foot pads and straps secure your feet.
* Wake-style: a shorter twin-tip board with bindings (boots) to secure the feet.
* Wake-skate: similar to a wake-style board but with no bindings and the surfaced covered by griptape.  Used for a variety of tricks. 
* Wave: a surfboard optimised for kitesurfing with foot pads and mounts for straps.
* Race: a directional board optimised for speed with longer fins

Twin tips

Twin-tip boards have become standard for use in flat water or small surf conditions.
Naish Haze 144cm
Advantages     Disadvantages 
* Easy to load into the car and travel with on planes
* Good for jumping - not too heavy
* Easy to turn - thin edges carve well
* No need to switch feet when changing directions
* Small fins are good in shallower water
* Not enough flotation to ride a wave under its own power
* Lesser wind range compared to a directional board
* Cannot be "paddled in" during a self rescue.
Factors to consider when purchasing a twin tip board:
* Shorter boards need more wind compared to longer boards; if in doubt get a longer board.  I am 6'1" and use a 144cm board.
* Shorter boards are better for jumping as they weigh less and create less centrifugal force while doing spinning tricks
* Longer boards are more stable at high speeds, and a longer rail is more efficient for edging
* Wider boards are easier to get planing compared to narrow boards
* Adjustable foot straps makes it easy to adjust them to accommodate booties in winter
Board size recommendations
Board size is quite variable - there is no real rule.  Smaller sizes are better for tricks, longer sizes better for freeriding and beginners.  As a guide
 Who  Height (ft)Height (cm)  Board size (cm)
 Peter6'1" 186  144
 Stuart 5'10"176 135
 Tarren 5'11" 180 127
Use a smaller board in higher winds for more control, and a larger board in lighter winds for better planing.
Write your name and telephone number on your board. If you lose it, it may be returned to you by someone who finds it.
Use a board bag.  It will protect you board from damage in cars, and prevents water and sand from the board getting inside your car.
You can find a fantastic analysis of twin tips board types here -

Wave surfboards

Surfboards, with our without straps, a favoured by kitesurfers who ride bigger waves.  Some prefer to use them on flat water too.  The extra flotation of the board means you can ride a wave under its own power.
Ivan Salmon riding toeside at Warrnambool, Victoria
Directional board on flat water
Peter Campbell riding directional board on flat water at Brighton Beach, Victoria
Advantages Disadvantages 

* Additional flotation is better for surfing big waves
* Better for self rescue - can be paddled in
* Better wind range - you can kitesurf in lighter winds compared to a twin-tip.
* Better for long downwinders
* Easy to go up wind, particularly when you move your rear foot toward the centre of the board.
* A surfing feel and experience on both waves and flat water.

* Being directional, to turn the board onto an opposite tack you either need to jibe the board, change from heel-side to toe-side riding, or stop and switch your feet around
* Larger and more solid - there is a higher risk of serious impact with the board and/or fins in a big crash
* Bulkier and more difficult to pack and travel with
* The pointy end of the board can be dangerous in impacts
* Easier to damage - particularly fibreglass Epoxy is stronger
* The fins are much longer and are easier to damage
* You are likely to need some board wax
* More difficult (and dangerous) to jump with *
Factors to consider when purchasing a directional board:
* Shorter boards have less flotation but may be easier to carve turns with.
* Most big wave kitesurfers use a tri fin (Thruster) board for optimum turning.
* Epoxy boards are much stronger than fibreglass ones.  Kitesurfing puts more load on your board than surfing.
* A strapless board can be used for both kitesurfing (once you learn how to use it) and for surfing, which is a good option for travel.
Board size should be approximately the same as what you would surf.  The rule of thumb is anywhere from your own body size, to your own body size + 2".
ie. Stuart is 5'10" and should have a board between 5'10" and 6'.
Practice riding a directional board on flat water before you venture into big surf.  Directional boards handle and turn quite differently to twin tips.  You tend to be more "on the water" rather than carving deeply into it as you do with thinner twin tips.  You use both the rail and the fins for turning. Master toe-side riding.
Take spare fins if you are going overseas to remote locations.

Race boards

Race boards are specifically designed for kite course racing, and excel in upwind and downwind/reaching speed.  Race boards can be hand made to order. The rocker, board outline, volume displacement, foot strap and fin positions are all designed for one purpose – upwind/downwind speed.
Airush Sector 60 race board
Naish Venturi race board
Advantages Disadvantages  
  • Very easy to go up wind
  • Very fast
  • Good flotation is better for self rescue - can be paddled in
  • Much better wind range - you can kitesurf in lighter winds
  • Excellent for long downwinders
  • Directional board so must jybe or duck tack to turn
  • Larger size - there is a higher risk of serious impact with the board and/or fins in a big crash
  • Bulkier and more difficult to pack and travel with
  • Very long fins are are easy to damage