Need some Amp help - a little new to properly powering speakers

Hello moskasudio,
   Let me start of by stating that my technical knowledge can be fit into a thimble,and still have enough room for a thumb!  That being said,how large of a room are you listening in? Also,how far are you seated from your speakers?  That information should be quite helpful. 
      
       Ray

The very first thing you need to know is that wattage rating on loudspeakers tells you exactly zero about how they sound.  All it tells you is that if you exceed that wattage, you can fry your loudspeaker.  

I think your current setup is actually quite well matched.   People who reside on the Audiogon forum will pretty much universally dislike both Japanese receivers and Polk Audio loudspeakers, but if you enjoy what you're hearing, then keep enjoying them.

If you really want to move up, then begin by listening to as many other loudspeakers as you can.  Visiting the local audio showrooms is OK, but your best bet is to meet other local audiophiles and listen to what they have.  Learn why they made the choices they did, both in loudspeakers and amplification.  

I have plenty of opinions myself, but what you really need to do is get more experience with the gear others own.  

moskaudio

 Impedance reaches a minimum of 3.75 ohms at 66 Hz and a phase angle of –47.96 degrees at 83 Hz.
Read more at https://www.soundandvision.com/content/polk-lsim707-surround-speaker-system-ht-labs-measures#fIW7rJB...

This indicates for them to sound their best in the bass, an amp that has good current delivery <100hz.
A good solid state amp that can keep increasing it’s wattage for every halving of impedance, is an indication that it can deliver current.

EG: A theoretically prefect amp that delivers current, none can do these prefect figures in real life, but some get close.
8ohm 50w
4ohm 100w
2ohm 200w

Cheers George

Moskaudio:  As said, it's not necessarily the amp's rated output, although higher output sometimes goes hand in hand with higher current.  High current amps and ones that have a high dynamic capability is what you want.  At "normal" levels, your used output wattage, will most likely stay fairly low, but when the snare drum cracks or the cymbal crashes, or the cannon sounds, that's when you need the headroom that a high current amp can produce.  Most speakers are not damaged due to high wattage, they're damaged due to clipping the signal.  A high current amp will always sound better than a high wattage amp made from IC chips.  The difference is night and day.  The impedance and the sensitivity of your speaker also plays a very significant role.