@twoleftears. One deficiency of looking for speakers first is that if the amp you have currently doesn't have the control over the speakers you are testing to demonstrate what the speakers under test are capable of. Last year I was looking to upgrade my system so I started by looking at speakers. One of the hifi shop owners suggested that I bring my amp and speakers in so I could get broader comparison. Making a long story short, When I heard my speakers through a resolving and powerful amp that was able to get the bass I'd been missing from my own speakers I ended up buying an amp instead. It was like I had never heard my speakers!!! The surprise to me is both amps rated for 100Watts RMS per channel. Old amp Rotel RA-1570 - new amp Simaudio 340dpx - speakers B&W CM5 S2.
So the caveat I have with starting with upgrading speakers first is make sure you have good enough gear to drive them when you are testing them so that you can tell that you are listening to the speakers and not deficiencies in the amp.
So the caveat I have with starting with upgrading speakers first is make sure you have good enough gear to drive them when you are testing them so that you can tell that you are listening to the speakers and not deficiencies in the amp.