First, where will you paddle?
Calm rivers or mellow rapids?
A combination of oceans, lakes and rivers?
Only the ocean, or only whitewater?
Second, while researching, decide:
How will you transport it, and where will you store it?
Do you prefer to sit inside or on top—or, a sit-inside tandem, or sit-on-top tandem?
Do you want a specialized rec kayak (fishing, kid-sized, etc.)?
Is any feature (e.g., locking hatch, weight capacity) a potential deal-breakers