$800 to spend on speakers, $1500 on whole system

The best quality for the $ is to avoid buying retail.

Right now I'm listening to $400 full range RCA MI-12480 Alnico (read about this, they don't use such powerful magnets anywhere near this price point if you buy retail anymore) drivers in a DIY wood open baffle. They sound far better than my $3,000 Monitor Audio GS 20s.

I would pair this to a vintage tube amp that you can buy for about $400. Something like a Fisher EL84. 

Then buy a pre-owned but recent model DAC.

Save a few hundred for room acoustic treatment panels from Stillpoints or GIK. These will make a TREMENDOUS difference to the sound. I would start with these first. GIK will tell you what you need. You can use 5D Planner to create a free rendering of your room. 

So so your budget could be something like this:
$200 panels
$400 speakers 
$400 amp
$500 DAC

All replies so far have recommended using passive speakers. Passive speakers connect a single external amp (which you supply) to a passive high-current crossover which is connected to the drivers.

I suggest an alternate approach. You should consider spending as much of your $1500 as possible on a pair of active speakers and the remainder on a DAC with volume control. Active speakers have a line-level crossover and a dedicated built-in amp connected to each driver. Although it is possible to build a good system using passive speakers, the technical advantages of active speakers are well documented, and recording engineers use active speakers almost exclusively. There are many options for active speakers at this price point.

Most active speakers take a balanced input (ubiquitous in pro equipment), so you'll want to look at DACs with balanced outputs. It is possible to find balanced DACs with volume control for $300 or less brand new from pro companies. Most of those will also include a headphone amp.

I suspect you'll get the most value from your money if you go down this road.

Pawadalla,
Johnnyb53, gives great advice. My alternative would be:

Musical Paradise integrated tube amp: about $380
Used Tekton M-Lore Speakers 95db/38hz/8ohm: $450
Used Sony S9000ES SACD/DVD/CD player as Transport: $295
Schiit DAC: $350 or
Belden 8402 interconnect: $80
Western Electric WE14 gauge speaker cable: $60

Best of luck, Rob

ccolby I agree which is why I suggested the adams. I thought the Nova Pre had balanced out my mistake. 

I put together a system for a friend using Spica TC50 speakers (with good, but generic 28" stands) and an Audio Refinement integrated. These have been out of production for a while and are both great sound and good value especially is a moderate sized room. Altogether they should cost no more than approx 8-900usd leaving a lot leftover for sources, cables, furniture, etc.