That is quite a decent budget.
Would allow something like:
HU: Pioneer DEH-P5750MP - $500
Splits: Rainbow CS265 'Profi' - $800
Sub: Image Dynamics IDQ12 - $400
Amp: Response 4x100 - $300
Total:$2,000
You have one big, beautiful saviour here, it's called 'Response'
The 4x100 will give you genuine outputs of 2x100w rms to your front stage, and 1x350w rms or so to your sub. Without response, youd need to spend possibly double this amount to get a 4 channel with that kind of power, with decent quality.
This leaves you with $1,700 to spend on your splits, source and sub.
The 5750 is a very nice source unit, is well built, well specified, nice to use (ive had a 5650 for years) and sounds quite nice. As a bonus, it even looks good! A great all rounder. Retails at $570 but getting it for $500 or less shouldn't be a struggle.
This leaves $1,200 to spend on front stage and sub. Plenty
First lets find you a really nice set of splits. How about some Rainbow 'Profi' splits? For pure sq, you really can't go wrong with a rainbow product.
This leavs $400 for a sub. Something like a JL Audio 12W3, or an Image Dynamics IDQ12 should be able to be picked up for that price, both being outstanding sound quality subs.
For the $2000 budget, without going second hand, that setup would be mighty hard to beat.