The ALR screen I linked to is AT. It's an option. It isn't as cheap as DIY options or even many other AT options, but it's one of two ALR AT screens I'm aware of and is the better of the two options.
It's up to you how you handle this. My own experience is that light control or an ALR screen is very important if you plan to watch movies during a time when it is light out. Most of my "theaters" were in dual purpose or non-dedicated spaces with windows. I had light control curtains with full blackout ability, but no matter what, some light always shined somewhere. The ceiling, floor, etc. Never could I black it out to the point of equaling no window at all. Even at night, light outside, even from the moon, was enough to raise the light level in the room a little. This reflects off the screen and raises the black floor a lot. In fact, I just did a demo in my dedicated room and needed to leave the door open (which would be the only way light could get in) and the impact on the black level of my AT screen was huge.
In my previous spaces, I tried everything and the only thing that worked was an ALR screen. Even a dark grey screen with a high brightness projector was not a workable option. This is why I say, you may want to consider an ALR AT screen. In fact, at one point I had some friends bring over their projectors to my then home theater space, a room with white walls and two screens. A unity gain white screen and an SI Black Diamond (one rolled in front of the other). The projects were my JVC RS1, a JVC RS25, an Epson 5010ub, and a Panasonic DLP model with DCI cinema mode, capable of around 10,000 optimized lumens. We tested at both 4pm when it was fairly light outside and again at 8 pm when it was dark outside (other than street lights, moon, stars, etc.). At 4 pm the Panasonic looked the best, it was most able to overcome the ambient light problems (again, with full light blocking curtains on all windows). The Epson was second best, it was the next brightest. It technically had the worst blacks, but both it and the Panasonic looked to have better blacks. None of them looked great, poor contrast with the white screen, but they all looked really impressive on the SI Black diamond. At 8 pm I expected the JVC RS25 to be the clear winner and on the unity white screen. What we found was not what we expected. While it clearly had the best contrast, none of them looked great on the unity gain screen because the light coming in the room (though very low) from outside and the reflections off the white walls were raising the black floor substantially. The Black Diamond looked the best because it was least affected by this. I kept the Black Diamond screen for years after with my JVC RS1. When I moved to the dedicated theater, I bought AT fabric and converted the black diamond, but I had a chance to compare both side-by-side for curiosity sake. In a truly light controlled room with very dark navy walls and no windows, doors shut, and no sources of light in the room, they looked nearly identical. The Black Diamond's reflective properties are different and it's a dark grey color so its blacks were still a little darker and it's whites less white (and it had a slight sparkle that the new SI screens have minimized quite a bit). Point is, in a truly light controlled room, the differences became minor, if anything, more just a difference in gain (the SI BD was darker).
So I concluded from all of this that really when it comes to projectors, light controlled means a black room with zero sources of ambient light at all. That anything else isn't really good enough in the sense that these non-dedicated spaces with light walls and windows will always compromise the black level a little bit. That this can be compensated for by using an ALR screen, and that it's even of benefit at night. If you do go with an AT screen that is not ALR in a space like this, the rise in black levels negates the benefits of the best projectors and you may want to consider a merely very good projector, in black levels, with a lot more brightness.
https://www.projectorpeople.com/scr...anu=Screen+Innovations&itmname=5+Series+Fixed
Here is a site with pricing to give you an idea what you are looking at.
What projector do you have in mind?