Hi, BJ.
ArthurDent is correct. We'll probably trip all over ourselves trying to help you out.

Before any of us can truly help you, you must first give us more information. Max already asked the first question that came to my mind, "Do you already have a subwoofer?"
Is the $2000 budget for the front L/R, center and two surrounds only, or is the sub included in the $2k budget?
What AVR do you have? (how many watts/channel?)
You said space is limited, so bookshelf speakers are necessary. What sized bookshelf speakers can your space accommodate (HxWxD)? Will you use stands for the speakers? Will the surrounds be mounted on the wall?
Will you consider 3.1 first with the idea of adding surrounds later when more money is available? [The advantage of this is you can buy a lot higher SQ with 3.1 first and only lose a little of the 'surround' information until you can add the surround speakers later.]
Have you considered (or heard) HT with front L/R speakers only? With good quality front left and right speakers supported by a subwoofer, very good quality can be enjoyed.
No, it won't be immersive like a theater, but 90% of the experience is in the front anyway IMHO.
Where are you located?
Welcome to AC.
Michael