What to upgrade next.


This is my first foray into the forum other than reading other's post. I hope respondents will be kind! I am at the very low end of audiophile equipment and many of you may not think I am there yet when I list my equipment. The economy has become better for myself and I am looking to upgrade but not exactly sure where to go from here. I am sure I will receive many different suggestions so I plan on taking the one suggestion that I receive the most and employing it. My equipment is as follows: Denon AVRx 3500H as my integrated amp which is boosted by a Bob Carver Cinema Grand 5 which pushes 200wpc. This powers my Polk Audio RTiA7's which are my music floorstanders. When I started upgrading I chose the Polk's as they seem to punch above their weight. After months on this site I am unaware of many people who extol the virtues of the Polks so I am thinking this may receive the most as far as recommendations. I stream most of my music from my desktop and laptop. The desktop sounds like an airplane waiting to take off. I am not independently wealthy but am looking to spend between 2-3 thousand if necessary. The one thing that gives me the biggest headache at this point is music delivery as computers have glitches and my angina acts up when the music cuts out in the middle of Alex Lifeson shredding his axe. My music files range from bad copies of MP3s which are slowly being replaced to HD Audio files. Thank you for any suggestions.
dadork
Dadork,
You may consider the route I took, buy use. I have 6 systems, 5 of which I listen to on a regular basis.  Other than the one I bought in 1984 all equipment was bought used. I enjoy all of them , some more than others. All told I have less than your  budget invested ( not counting the 1984 purchase ) I suggest that you use a good streaming service ( Qubuz,  Deezer, Tidal ) and as already mentioned, improve your internet. A wired connection sounds the best to me.
My up grades would be a better streamer & dac ( currently a Yamaha WXC-50 ) & room treatment .

Dadork, have you considered a three or four steps to audio heaven?  A streamer, yes.  The rest....Besides the streamer, a two channel pre, with the best specs you can afford.  There are a couple of Meridian 2chan audiophile pres on Ebay at 1200 and more.  Use the Carver for a basic biamp on the speakers.  Next step a dedicated stereo amp.  Then replace your speakers, mine are Martin Logan or Magnepan.  By starting with the electronics first, you will know how your system synergy sounds prior to adding the big variable new speakers.  You could eventually use the Carver to power 4 or 5 swarm subs.
Try using a TV streamer like Apple TV or the others to download Tidal.  I stream Tidal from an Apple TV via HDMI into a decent AVR and an external 2ch amp drives LR speakers. But the Tidal service was a real revelation to me a few years ago.  For me the Bluesound Node 2i is next on my list.  I encourage liberal use of stores’ return policies.  
Hi Dadork,

Because you’re operating your system for both music and movies, my advice will diverge from the stereo purists here.

1. Buy a leviton hospital grade 20A electrical outlet. $10

2. Buy a video streamer that will allow you to cast from your phone over WiFi--either the Chromecast Ultra or Nvidia Shield TV (which has chromecast built in). Both of these video streamers will allow you to cast movies and music from your phone. In addition to your personal HD tracks, I recommend subscribing to either Tidal or Qobuz to get CD quality and higher recordings. I use Qobuz and a chromecast ultra in my home theater. I also have a separate stereo system in the main room that I cast to.

3. Buy a low noise power supply for your video streamer. iFi has a variety of options to meet many voltage and amperage requirements.

These recommendations are super affordable, should increase sound quality, and will also level up your experience. These building blocks will also give you a good benchmark from which to judge future streamer/home theater bypass upgrades. 
A streamer and a good dac would do a lot. I don’t think it would be a waste.