Just confused about where to start

If you want imaging and clarity without brightness the Elac Uni-Fis could be right up your alley.  

A subwoofer is about more than visceral bass, it also helps unload a lot of work from the amplifier and can ease positioning issues with the mains (especially if you have to place them near a wall or on a desk where having too much of the bass coming from the mains can cause the sound to be muddy).  A pair of bookshelves and a subwoofer can oftentimes outperform towers, especially in a smaller room like yours.  

Plus, you can always adjust the gain on the subwoofer to apply the amount of bass for your preference.  I'm not a bass-head either, but I enjoy the fuller sound that a subwoofer provides.  With the room correction and auto-blend functions of the Elac amp I don't have any boom, just nice full music from top to bottom.

For $1,500 this is the way I'd go:

Speakers: Elac Uni-Fi UB5 (currently on sale for $350 @ Amazon, normally $500/pair, and they'll easily best speakers costing quite a bit more)

Amp:  Elac Element EA101EQ (currently on sale for $620 @ Amazon)

Subwoofer:  Either SVS SB12-NSD ($449) or Rythmik L12 ($539)

You didn't explicitly mention a subwoofer, but if you're going with bookshelves, and want to do things headphones can't do, one of the big things being tactile response from the music, you want a sub.  The beauty of the Elac Element integrated is that it has built in subwoofer integration with automatic room EQ and subwoofer blend including phase adjustment, so you can get the speakers and sub working beautifully together.  It also has a built-in USB DAC so it's easy to hook up to your computer.  

I have the UB5, SB12-NSD, Elac Element comb.  I use it for my computer audio setup and it's excellent.  The Rythmik sub is certainly worth a look though.  Either way you're within spitting distance of your budget.  

The nice thing about headphones is that they take the room out of the equation. For speakers the room, furnishings, treatments (if any), and positioning can make a big difference.

Is this a dedicated listening space or are going to be practical concessions in terms of placement?

As far as amps go, you’ll want something with enough power to drive the speakers you choose and that can handle whatever the impedance of your speakers is.  

Most integrated or standalone amps are fine with 4 ohm loads, and the vast majority of speakers don’t present a load appreciably less than that.  

Since you have a small space you aren’t likely to need tons of power.  

I kind of surprised you liked the Motion 15s considering the sound signature you mentioned upthread, I found the ML Motion series to be unpleasantly bright, but it could've been set up poorly in the BB when I demoed them, there's a ton of variation between different stores, and even between speakers in the same store with them.  The first time I checked out the ML Electromotion ESLs I thought they sounded like junk, heard them at a different store and they sounded great. 

The LS50 Wireless is supposed to be superior to the unpowered version, so it could have been a setup issue.  Having built-in DSP and amps matched to the drivers should actually lead to a performance edge.  I've only demoed the unpowered version and I thought they were nice enough, but I didn't think they sounded any better than my Elac Uni-Fis and weren't worth anywhere near twice the price.  They are finished much more nicely though.  

If you're going to add a sub (which again, I do recommend) make sure whichever pre-amp/amp or integrated you choose has built-in bass management and some form of room EQ.  Aside from the Elac Element there's also the Paradigm PW Amp and the Martin Logan Forte (which is just a Paradigm PW Amp in a Martin Logan case) both of which offer great subwoofer integration and ARC room correction.  They don't have the built-in USB DAC or a remote control like the Elac Element, however, you have to use a smartphone app to control them.  

Snell made some great speakers back in the day.  They also took the time to match drivers and even hand-tune crossovers for every pair to account for any variance in the drivers so that the speakers matched as much as possible.  

The new Yamaha integrated amp is worth checking out.  It has bass management and YPAO room correction, plus more wattage than the Elac Element I mentioned upthread.  

https://www.soundandvision.com/content/yamaha’s-new-21-channel-receiver-boasts-ypao-room-correction