a first integrated amp to build a system around

I don't know if this is the right place to ask this question but I can't find a better one. So here it goes...

I have done some research trying to find the best amp/speaker/cd combo to build my first system.

My requirements are
total system cost < $2000
phono input
amp with good DAC for iPod/computer input
disc player recognizes HDCDs

I have a list of components but have no idea how to start narrowing it down or finding the right pairings. I almost certainly cannot go out and listen to all of these so I need to narrow my options before I go out and start listening. Starting with an integrated amp seems like a reasonable thing to do. Can you help me make my lists shorter?

Here are my lists of components:

Integrated Amp:
NAD D 3020
PS Sprout
Outlaw RR2150
Music Hall a15.3

Emotiva Airmotiv 4s
Direct Acoustics Silent Speakers II

Disc Player:
Music Hall c-dac15.3
I almost certainly cannot go out and listen to all of these so I need to narrow my options before I go out and start listening. Starting with an integrated amp seems like a reasonable thing to do.
Sorry but I disagree. Starting with the speakers sounds like the most reasonable thing to do. After you settle upon the speakers that sound best to you, then select the amp that will properly drive those speakers to whatever sound levels you're comfortable listening at without any fear of clipping.

So suggest you start auditioning speakers immediately, even if they are not the ID brands you list above. BTW, why those? Have you heard them? The Airmotives are active speakers meaning you don't need an amp. The Direct Acoustics are 6 ohm nominal, 4 ohm minimum with no sensitivity figures published. From the looks of these, neither is the ideal match for the amps you mention.

So before you spend a dime, suggest you google the two big speakers specs, impedance and sensitivity. Learn and understand them and how they relate to an amp. Then go out and audition as many speakers as you can paying attention to these specs, their driver compliment and how they ultimately sound to you. You'll be on your way to spending your 2 grand far more wisely.
+1 Paraneer. Auditions are the best way to go, and you really should start with speakers. Electronics have a comparatively smaller influence overall. In this case, time spent up front will really save you money.

Good luck & happy listening!
Speakers are the key at this level. I would consider the Magnepan MMG(new or used) or the Silverline Prelude(used). Look(might take some time) for a used NAD S300 or a Classe 151. Both these amps are of high(build/sound) quality even if there 10+ years old, $750 should be enough to find a nice unit. Save money on the digital front and consider a Sharp DX-670/770 or any Sony ES player, a nice working Sharp should cost <$100 and some Sony ES players can be found for <$200. Cables are important, Signal Cable Reference(silver)can't be beat when regarding price. With this set up only the CD-Player will need to be upgraded when your ready to improve your system.
Without sounding scolding I also agree that system building starts with speakers. They are really definitive in the way your system will sound. If I had to choose the non speaker parts I recommend buying the Music Hall gear. I bought my first "higher end" system over a dozen years ago and bought an MMF25 CD player. Post divorce I am listening to it now, no issues. In the end it is better to pick the gear that your speakers work best with.
when you get around to re-looking/listening add the Peachtree series to your list. 65, 125 or 225.
Would help greatly to know what sound reproduction characteristics are important to you, what type of music you listen to and how loud, etc. That said, agree with others that speakers are the place to start and then choose an amp that matches sonically with them and that can drive them properly. Then go from there. If you don't get speakers you love you'll never truly love your system, so do whatever you need to do to get that right.

If you lean more to classical, acoustic jazz kind of music where imaging, soundstage, ambient cues, etc. are important I second something like used Silverline Prelude or Minuets. Very good all arounders that can do the audiophile nuance stuff well. If you're more into loud rock and need slamming dynamics something like the Tekton Mini Lore or one of their larger models used would be a better choice. Anyway, as others have said, it's best to go out and start listening to some speakers with your music so you can start to identify what you like and so you have a more defined idea of what you're looking for. More useful and productive than reading our blabber IMO. Best of luck in your search, and have fun with the whole process. You'll learn a ton, which makes it even more fun.