Phew. Lots to unpack here...
Your sub is what jumps out at me first. Klipsch subs for the most part are pretty lacking.
Your TEAC seems a bit underpowered but depending on room size and distance from your speakers that may or may not be a factor. Curious tho, why that particular model? A good mid tier HT receiver would have more power, connection options, bass management, room correction, etc. I use a pc for my music and HDMI to connect it all. Easy peasy. Does the TEAC receiver offer any kind of bass management (like the ability to set a crossover point between speakers and sub) or is it just a sub out?
I can't find any meaningful specs on your Polks. They don't list fr or sensitivity on their site, but I generally don't look to Polk when speaker shopping. I think there are better sounding options for the prices.
Klipsch can make some good speakers, but again, they're not my usual go to when speaker shopping. I'm not familiar with your particular model, but they're powered right? They're a whole different animal and aren't using the TEAC's onboard amps at all.
I haven't found a streaming service I was happy with in terms of sound quality. When compared to my lossless cd rips it's no contest. I much, much prefer my rips. They're just cleaner and clearer. Amazon Prime HD music came close, but my own native content still sounds better. I gave them a shot with a free trial offer and cancelled as soon as it was up.
Finally, speakers and subs are definitely where it's at for sound quality. Amps and receivers will for the most part sound similar enough, with a lot of differences in the way they measure falling outside the range of human hearing. A lot of folks get tangled up in trying to make improvements by rotating through receivers and amps and that's a good way to spend a lot of money while driving yourself nuts trying to hear differences between them.
So, what are your listening habits volume-wise? What specifically are you not happy with right now? Placement, positioning and room have a huge impact on overall sq too. A pic of your setup and room might be helpful.