Speaker and amp pairing

Here’s how I think of speaker sizing and amp matching:

1. how big is the room - size the speakers accordingly
2. how loud do you like to listen - speaker sensitivity and thus amp power should be able to produce the desired db/SPL (can check with any calculator)
3. what’s the nominal impedance of the speakers’ bass woofers and midwoofers? This is a function of the size and number of the drivers, and the crossover topology. Generally, for a standard 2-way with 6.5" driver, the impedance will drop to 3-4ohms at its lowest points even if rated 8ohm nominal. If nominal impedance is 4ohms, well, it’s likely to drop even lower. Be very careful about the current demands for 4ohm nominal speakers - look at the amp design and specs and it should be easy enough to say a NAD 3020 or flea-powered tube amp is going to have a bad time.

Assuming there are no technical red flags, the rest is timbral matching and sonic preferences.

If you aren't absorbed into the tube vs solid state thing, just buy a larger 100W to 150W per channel solid state amp from a reputable audio brand and you should be okay.  Even new NAD and Yamaha larger amps sound okay vs older amps from 20 years ago.  A good 100W/ch amp will drive even lower sensitivity speakers.  Class A/B generally sounds better for the money, due to the larger linear power supply.  Usually lots of used integrated amps (preamp + amp together) for sale here which often offer larger output than receivers which can focus on features you may not need (bluetooth, airplay, etc).  A $500 used integrated from the last few years would be much better sounding than a new $500 (entry level) denon receiver.  
Brad 

There are lots of variables in play, but I learned a long time ago that not all watts are created equal, and that the measured specs for many amplifiers don't tell the whole story about how well they'll actually drive a speaker.  Nor the do specs indicate how an amp will sound.  Some of that is due to the fact that speaker impedances vary a lot, but most don't pose an unusually difficult load for a decent amp. 

If the nominal speaker impedance is rated at 8 ohms, most speakers will do fine with a well designed amp that has good current flow, unless the speaker is known to have a very low or complex impedance.  If nominal impedance is 4 ohms, you'll want an amp that control a low impedance speaker well.  It shouldn't be too difficult to research if any speakers you're interested in are known to to pose very low and/or difficult to drive loads, or how well a particular amp handles more difficult loads.  

As long as a few minimum impedance requirements are considered, I've always tended to focus more on how the speakers and amp sound together, with more focus on the speakers first, then try to find an amp that's capable and that I like the sound of.  It can take time, and trial and error, but can always bring a lifetime of enjoyment when done well.  

I just switched from a 50 watt a/b amp for a 150 watt Class D amp at 8 ohms. My speakers are 4 ohms and this amp will provide 250 watts.
my room is  small 12x14’ and not at loud levels. The higher power amp provides lots of clean power - bass so clean and accurate and zero heat!
not my first class D amp-

you have to listen ! And with the absence of audio salons , a good choice is impossible via mail order! I sent back the 50 watt/ ch amp and it’s a PIA  and only by luck did the next amp sync!

millercarbon and knotscott make the most sense here. Impedance, watts, sensitivity, etc., all come into play. Looking at those numbers and pairing with an amp certainly come into play. However, numbers are that,,,just numbers.
An example....Years ago I was playing Klipsch speakers(Reference line) through a not lower line HK receiver. Watts and all those numbers seemed compatible. The sound to me (in those days) was pretty good. Then, I got a good deal on a NAD integrated and hooked them up to those Klipsch speakers. Sounded like I threw 3 Army blankets over each speaker. Not wanting to ditch the NAD amp I investigated other speakers. PSB was the final result. I believe the two companies are, or were combined.
The main point here is that no matter how long you compare and try to match numbers, there is no final answer until the speakers and amp together are listened.