What to upgrade next.

I would think a good DAC would be a great place to start. The Musical Fidelity V-90 is a real value for $299 new. And since you mention your desktop is noisy, you might look for a Software-based fan controller. My iMac In my listening room was very loud. Mac’s Fan Control lets you choose the RPM that cools while holding down the noise. I assume there’s something similar for PCs.

@dadork
Welcome to the club. My general advice to you is to do a lot of research before you buy. When you finally do, buy second hand. Some of us are further up the chain than you are, but the feeling to upgrade is universal in this hobby. So take advantage of that. Keep in mind that price is not always proportional with sound quality although unfortunately it often is. So good luck, have fun and try to spend more time in front of your equipment than behind it. 

I would begin with a separate 2- channel preamp with HT Bypass. Run all your music sources through it and the L/R preouts from your AVR into the bypass input. Used preamps on Audiomart from Rogue, Odyssey, VTL, etc. can be quite affordable and will get you going. Ditto on Node 2i for streaming. This assumes the Denon has L/R preouts. If not replace it with one that does 

Hi,
First of all, if you have an Apple computer get Channel D's Pure Music program. If you have a PC get J River's program. If you do not have one already get a good USB DAC, there are many on the market. You are already getting rid of the MP3 files. I generally use HDTracks for down loads. Next sell the Polks and get a pair of Klipsh Cornwall IV's This will make you VERY happy for a while. When more money comes in down the line get either a DEQX Premate or Anthem STR . These are digital preamplifiers with huge power. Next comes an amplifier. With the Cornwalls you only need 100 watts/ch and I would recommend a tube amp such as a Carver, Manley or Mcintosh. Finally, two subwoofers. You would already have the best crossovers in the preamps plus room control so all your need is a passive sub. If you are handy, building a sub from Parts Express would be tops and very cost effective. Now you can just collect music:)

Well given you are now considering a 10K system the 'plot thickens'. A very good system can be had at this price level.

I have a couple questions that will help in providing advise.
What is the room size where this system is to be placed?
What is the timeframe for completing this system?
What computer and file type are you using?

There are many ways one can approach this. I also started towards a 10K system, spent 8-9K and ended up with a 15Kish one. Bought used or dealer demo equipment, made my own room treatments, did much research. Now working towards 25K. As I have a system that truly satisfies, I started my upgrade path with the source. I believe in your situation this approach would serve you well also. In my case I felt the need to get a DAC and transport for CD playback in addition to using MAC computers as servers. I also have a DVD player for movies, however playback is via 2-channel sound only. I not much into multichannel playback for movies as I don't wish to build a theater room. I find 2-channel for movies to be quite satisfactory in my music room. 

I have and still use a Macbook Pro and a MAC Mini as a server and streamer. As a server I rip CDs as AIFF files (equivalent to WAV)  and play back using the Channel D Pure Music program. As a streamer I only have used Pandora or Spotify as I stream to find new music and purchase the CD. I play back CDs via transport and DAC. There are other streaming sources , Tidal and Qobuz are popular, that stream CD quality or higher rez music. I would advise that you research servers and streamers under the digital topic here on AG. I think what you will ultimately want is a server for file playback that also serves to stream. 

My advise to you is to 1st research the use of server/streamers as your primary music source as that seems to be your interest. I would bank most of your 2-3K while researching this and in the meantime purchase a used  budget DAC to play into your Denon AVR. Knowing more about your computer and flies would help here. 

Following that I would get out and listen to as many speaker amp combinations to get a feel for what truly moves you. Keep in mind that speakers play into a room. Pairing them to your room, and treating the room as much as possible to play well with the speakers goes along way towards getting the most out of your system. Following that your amplifier must mate well with your speakers. I would look for speakers that are at least 87dB sensitive and not difficult impedance wise. Another area to research.

Save your money and be positioned to purchase the right product at the right price that fits your predetermined audio scheme. Having an understanding of what your want is paramount to getting it.

Again enjoy your quest. Let's keep the dialog going.