I should start with speakers. This I know. I’d like to establish a new system.

@toontrader, when I read @tomcarr 's comment 

Acoustic treatment.

The room will dictate at least 50% of what your system will sound like.

followed by @hilde45 's

If I was in the position of the OP, I do the following:
1. Try to size up the assets and challenges of the acoustics of the room. 
I'd lay hands on whatever gear I can find to listen with.
I'd listen, position, and once some reasonable positioning is established, I'd measure for frequency response.
2. With the information gained above, I'd try to treat the rooms major flaws, focusing first on 20hz to 300 hz, since those frequencies have to be mastered before dealing with the rest of the range. I'd work a bit, next, on 300hz-20khz.
3. Having brought the room to a baseline of decent response, I'd do a bit of research on speakers and amps that will match my tastes and my room.
4. Next, I'd start borrowing speakers or buying, used. I'd get a decent solid state amp (used, hopefully a keeper) that can drive a bunch of speakers.
That would be the "launch sequence" to getting the basis of a good system going, in my opinion.
Sum:
Get the room ready.
-Try speakers and amp.
-Get final speakers.
-Get final amp.
-Figure out how to optimize the rest (preamp, DAC, cables, power, additional   treatments, subs)

I suspect that many of us got the first part of 'Sum' bass ackwards either long ago or too recently to be entirely comfy with, so....

New home?  Lucky....built to a plan of theirs' or yours'?  Make a sketch or copy that area of the plan with door/windows/ac plugs with the ceiling detail(s).  Dimension all.  Have it on phone or laptop when you prowl the B&M's.  Consider the what, where, and why.
Buy used for test purposes; if you absolutely must have a That, work on timing for a demo in situ. Or consider a gently used part of the (never, really) Final Outcome.

Have a great time. ;)  👍😎 J

@hilde45 OMG, I shrank your post. 🙄

@hilde45 You have given some great advice

@toontrader let’s circle back on your room dimensions. They could be a real challenge or you could do something really specia. The long wall may very well play into an outstanding fit for large Magnepans like the 3.7i and a sub(s), and something quite different on the narrow end, maybe British and more ’intimate’. KEF F, B&W amd Monitor Audio all offer excellent choices for that application. It really is a unique opportunity.

On the other hand, it think the room is just too long to be well served by a single pair of traditional cone speakers. Horns biggest benefit  is controlled directives, which could make a very small listening window if used on the long wall. Cones might have broader coverage, but thats a lot of room volume for them to fill with the amps being mentioned. 

Your on right path with the Volti's, horns don't require loads of power which helps to keep total costs down. Horns specialize in bringing performers into the room perspective, pair them with some 300B SET amp and you'll have the beginnings of a great system.

Starting with speakers is how I've always built systems, matching amp is absolutely necessary at this point. I also like the open baffle suggestions if you're after the performers in room perspective. They may require more from an amp so that's a consideration.

Over many decades I evolved from box to open baffle to horns, horns matched with SET amp is magic for me. Again, the Volti's would be a great initial choice, they're an evolution from Klipsch Heritage, that's saying a lot.

$20K budget means you will need to buy used to get max value. Even then you are going to have to be a sharp negotiator. 

I'd start with listening to different speakers where you can- dealer, friend, etc. Listen to the leaders in their class- ie: Maggies, Wilson, Sonus, Bryston.  Each type has a "voice" that is somewhat consistent throughout the type (ie: Electrostatic vs. cone vs. hybrid)

Once you pick out "your sound" buy the best speakers you can afford. IMO speakers have the most dramatic and identifiable effect on your rig. 

The next is a toss up- The saying  "put your money in your DAC" saying has a lot of truth to it.  Then your amp. IMO tubes are best for depth and soundstage but there are some fantastic SS amps out there these days that get pretty close. 

Expect about a year to get this all right- and maybe some mistakes along the way. The process is fun if you you're a journey kind of guy. Most here on these forums are.