Step 1: What shall it do?
Rule 1: Brushless Motors are twice as efficient than brushed on lower power levels(under 65%)
Rule 2: More Motors means more power and more lift!
Tricopter: The little baby brother of the multi-rotor family. Its one of the easiest to build and the cheapest to build, however when it comes down to performance its motors take the most strain because they are running on a higher throttle than any of its other siblings leaving it with low flight time and low lift capabilities.
Quadcopter: One of the most popular craft in the multi-rotor family. Its a little more challenging to build and a little more expensive. The quad is only a couple grams heavier with the extra rotor but that extra rotor gives the quad a huge boost in lifting capabilities and flight time. If a motor fails though the whole vehicle will go down.
Hexacopter: In-between a quad and an octacopter. It can be difficult to build and more expensive to make and it also takes more ground prep time then the quad or the tricopter because it tends to have multiple batteries. It can carry a much heavier load than the quad can but it may require 2 batteries to achieve the desired flight time you want from a multi-rotor. Even if one of the motors fails you will just lose yaw control of the aircraft but manage to stay flying.
Octacopter: The big brother of multi rotors. It is the most challenging and the most expensive to build. It can take the heaviest load for the largest payload you want on it and can have up to a 40 minute flight time. Before flight it can require a lot of prep work as some octacopter a can take up to 4 LiPo batteries.