Arduino is an easy way to mess around creating your own flight controller
There's already one's available such as
this which is effectively an arduino with MPU6050 6 axis gyro/accelerometer and all the right pin connections
Note this has minimal facilities so you have to actually fly it yourself (no GPS etc) !
Speed controllers (ESC's) usually need PWM signals to control them but the ATmega (8bit) chip has limited PWM options but can still be used OK
Most flight controllers now use 32bit processors which are faster and can hold larger control programs with better hardware facilities
For control, it's probably best to start with standard rc Tx and Rx units
As for choosing actual components such as ESC + motors/props, alot of this depends on the size of the quad you're wanting to build
Maybe best to look into
RCGroups forum for info/help
The 2200Kv (Kv is 1000rpm per volt) motors are typically used on small drones, now often used for racing.
Hobbyking is a good place to get cheap rc kit.
It's useful if you should break a part you can replace it with an identical part which may be difficult if you buy random bits off ebay
There's lots of things you'll need, power connectors, suitable wire, and don't forget LiPo's (batterys), they will also need a charger
And buy spares of breakables, especially propellors
If you're unlucky, a crash will break the motors quite easily and sometimes can cause the ESC's to go up in smoke
This lot can add up to quite a bit, hence the cheap Ready-to-fly drones are an easy option