What's wrong with my setup?
 

I bought a new E-flite Mini Ultra Stick PNP. It came with a Park 450 motor, and E-flite 22 amp BL ESC installed. I bought a E-flite 3S 11.1V 2200mAh 30C battery (recommended to me by the LHS guy) to go with this setup. My problem is, when The motor is at a complete stand still, and I gun the throttle, it doesn't instantly run up to RPM like another electric I have does. Instead, it lags for a second, then spins up slowly and then gets going fast. But there is a big hesitation before it gets up to the proper RPM's that coincide with the throttle position. And if I leave it at full throttle, within 10 seconds the motor cuts off completely. If I cut the throttle all the way and then increase throttle, it starts working again. The motor gets hot very quickly. I'm not too familiar with electrics, and that's why I wanted to start with one that was already set up for me for the most part. But I'm wondering if something is wrong with my setup. Can anyone tell me what's going on with this?

From what you describe it sounds like your ESC is programmed for a Heli where the high inertia of a rotor requires a slow start up to prevent overloading the motor and the gears, however according to the instructions the E-flite 22 amp BL ESC is a 'simple' type and does not have this feature! This is a puzzle?

The motor will get warm but should not get hot too quickly particularly as in the mini Ultra Stick it is right in the breeze out front.
What prop does it have on ?
Too big a prop will over load the motor it will then get hot and eventually burn out!

Yes, there are no settings on that ESC for slow-start.
Check all of the connectors .
Yes too large of a prop will overheat the motor so you should be running a 10x6 or 10x8 prop.
If the prop is good then I would suspect the motor.

USMC2111
Just a thought but there are two versions of the Park 250. One 890kV, the other 1200kV.
The correct props would be quite different.
Do you know which you have?