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

I agree with the peach tree recommendations. I had a decco in my office driving a pair of very modest PSB bookshelf speakers, and the combo was great. I had my computer plugged into the peachtree unit via USB.  The Nova is even better.  

There is a refurbished nova 65se on eBay for $699.  I would jump on that.

http://www.ebay.com/ulk/itm/321936858478

Get a $95 transparent performance USB cable, and you have $700 for speakers & cable.  A short run of audioquest type 4 is a nice budget cable, far better than basic cable, and that should run $100.

for $600 speakers, I would look at these Totems:

https://www.audiogon.com/listings/monitors-totem-acoustics-model-1-2016-02-06-speakers-33434-boca-ra...

Good Luck!

just realized those Totems may be in need of repair for that price.  Worth looking into though, seems like a very good price, and the seller is not sure if there is a problem or not.

While most of us can put together a really satisfying system with a budget price to performance ratio, a beginner seldom does this on his first try. For that reason, an integrated USB-capable DAC/integrated amp is a good start. It eliminates cables between the DAC and line stage, and between the line stage and the power stage. There is also less clutter and more integrated operation. And this is at no sacrifice (and possible gain) in sound considering the budget.

The OP seems to lean toward small floorstanders, and I think that’s a good idea. Floorstanders don’t need stands, which add substantially to the cost at this budget. Floorstanders are also more efficient, fill a space more easily, have more dynamic range, and bass extension

This is the OP’s first stab at a quality audio system. I think getting new equipment with a warranty and return period is preferable to a distance purchase of used equipment of unknown age and condition. Sure, many of us know how to put together a used or pawnshop system for a low price, but most of us learned by doing. My first stereo was a new store-bought Altec-Lansing compact, with a receiver and turntable in a single enclosure and a pair of matching speakers.

I got a lot of enjoyment out of that system, but within 3-4 years I’d moved up to a Tandberg reel-to-reel with excellent phono stage, SAE line stage and amp, direct drive turntable with top-line Grado cartridge, and time-aligned floorstanding speakers. I got 11 years of good times out of that second 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.