Speaker and amp pairing

sensitivity, response, sonic end product, physical end product, cost -- it is all about a fairly complex set of tradeoffs folks

High sensitivity speakers including big horns as I use always have more life like dynamics, immediacy and realism to me.

Some nice thoughts here - thanks so much!

Tonal profile, sensitivity, impedance and recommended power rating are largely what you need to consider though recommended power rating is less of a concern than you might think.

all of this needs to be taken in context of your room and your taste.

Impedance is a critical factor and can’t be ignored.  The lower the impedance, the more current is required to drive a speaker she effectively, the harder it is to drive.  You should find the minimum impedance of the speaker and make sure your amp is at least stable at that level.  If you listen loud, make sure it thrives at that level.  
I had speakers that had a minimum impedance of 1.7ohms and amps that were not rated for that impedance.  Blew lots of fuses.  My sales rep at the time was a jackass and I new nothing as I was seventeen.  

Regarding sensitivity, I have nine pairs of speakers, one has a sensitivity above 92dB.  This is one persons very specific view on sensitivity and affinity for a specific manufacturer.  Millions of people have lower sensitivity speakers and are perfectly happy.  That being said, the lower the sensitivity, the lower the volume output in relative terms so you will need more power which can be limiting depending on your room.  
Regarding power rating, minimum is more important than max unless you listen very loudly for a long stretch.  

Under powering a speaker will leave the sound thin and lead to clipping and distortion.  In extreme cases, this will cause the voice coil to get extremely hot and expand and will lead to a permanent rattle and require driver replacement.  This is uncommon.  
This is driven by room size and proximity to the speakers based on sensitivity. I sell speakers that literally have a power rating range of 25w to like 800w. What do you buy?  Depends on the room and your listening habits.   
You have to pick right speaker for the right room and then power it based on your tastes.  Simple concept and if you are honest with yourself about what you want/need, you will be very happy.  
 

My .02 Depending on your budget and your passion for the music. There are hi rez speakers out there that require component matching to get their best sound, also try to find 3rd party measurements of speakers because most companies fudge the sensitivity numbers. Too much power is always better than to little and again...