
Valerion
VisionMaster Pro 2
Great picture/gaming, but RBE and no lens shift are dealbreakers.

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Not 100% sure what you meant by the air purifier setup, but I get the idea of a movable stand. In practice though, I found it way easier to just settle on a fixed placement and screen size first, then work around that. I picked up a jmgo n3 Ultimate this year and it’s been solid so far, bright enough for daytime-with-curtains use, easy setup, and I’ve just been using the built-in speakers without needing anything extra.
Check out what is within budget from JMGO. Not sure. Most of their stuff is well reviewed. The Optoma PH31 is a 1080p projector with 1,500 ANSI lumens and is absolutely worth taking a look at. Incredible value for the money. There are a couple of lamp-based models which are brighter and potentially better overall for home theater with the BenQ TH575 and the Optoma HD146x. Many people use them for their home theater setups. Lamps may be going out of style, but they are cheaper projectors with a lot of brightness and solid image quality. If you have some other specific models on your radar, ask specific questions about them. Be aware of complete no-name brands. DLP projectors are where the money should be spent at this price point.
I'm a fan of JMGO products, and they have all reviewed strongly over the years. But, the Optoma PH31 absolutely is the best deal going right now. By far. JMGO regularly has 4K models which are very well priced, but they also tend to be kind of dim for the money. More 'portable' than 'lifestyle'. They don't work well in rooms with ambient light. But, they are still incredibly affordable. Their N3 Ultimate, which is three times the money, is still an insanely good value for what it is.
You don't see 4K projectors on Amazon for 250. You see people lying to you for 250, and stupid people that never bother to ask talking about their amazing deal $250 projector. No. That's not how it works. The cheap, no-name, crap quality projectors on Amazon/Temu/Alibaba, are pretty much all crap. They use a single LCD panel, like you find in your mobile phone. Not the good mobile phones either. The cheap garbage ones. The $300 no-name LCD projector shares more in common with the $40 LCD projector than it does with the cheapest BenQ or Optoma out there. You should be looking at only DLP projectors or maybe an Epson model, though they don't make much in your price range that's worth looking at anymore. XGimi, JMGO, and Valerion are excellent options. If ceiling mounting, the XGimi Titan Noir is a really solid option for home theater. The JMGO N3 Ultimate may be an even better overall deal. Projectors don't perform well in ambient light, so if you are looking for a family room setup, it is cheaper to buy a 100" television than any ultra-short throw (UST) projector with a matching ultra-short throw, ambient light rejecting (UST/ALR) screen. If you are on a tighter budget, the low end starts with the Optoma PH31 which is a 1080p DLP projector with 1,500 ANSI lumens. A really good value for the price. Cheaper DLP projectors are the XGimi Horizon 20, or Nexigo Trivision Ultra. The Horizon 20 would probably be my first go-to projector for the money right now. Check [www.youtube.com/thehookup](http://www.youtube.com/thehookup) for quality reviews. Check [www.projectorcentral.com](http://www.projectorcentral.com) for actual need to know information and articles about front projection. Do your homework before you spend too much money. Make sure you understand: Throw distance, lens offset, digital zoom, optical zoom, keystone correction, lens shift, and understand how to use the throw distance calculator at Projector Central completely.
The Horizon 20 is a heck of a good projector for the money. If you can swing it, the JMGO N3 Ultimate is a best. Far brighter, with more zoom range and lens shift compared to about anything else in that price class. I'd likely take that over almost anything else right now. Nothing wrong with BenQ, but other smaller manufacturers are making them look very dated on many models, but they still look good. Just outclassed by the competition.
The throw distance if way too far for such a small screen. You'd have to use a ton of digital image correction, which will cut resolution down by 50% or more and throw all that light away as well. A TV is by far and away the proper solution at the size you are working with. But, you can use any projector with digital zoom on it and you'll get typical results. JMGO has their 4K models on sale right now, and they are about as cheap as you can get while maintaining a high quality image. So, I'd try one of those, and if you aren't happy, then realize you aren't getting 'better' really.
Just got the JMGO N3 Ultimate a few weeks ago. Coming from a cheaper setup the thing that stands out most is how complete it feels as a package. That's what the $2k-3k range actually buys you.
If you’re just trying to get a solid 120 setup and not keep messing with it, I’ve had some early time with the JMGO N3 Ultimate and it’s been pretty easy to deal with so far. Brightness has looked solid and the image has been clean without much tweaking. It hasn’t felt like a rabbit hole purchase.
A great little video on why a screen is not always necessarily needed (going from a fairy expensive screen to just the wall) for an amazing image. https://youtu.be/Xaj-xeYFBfo?si=tdUZroN64jRzZ7Sl A darker color will absolutely make a difference for your light spillage...if you want any type of home theater experience with contrast that is quite important. I would even go as far as a carpet for in front of the screen to further reduce that light spillage. https://a.co/d/01CPuaGu If you do not want to paint your walls (which again is not for everyone) then another solution for around the screen and ceiling is this felt which almost completely eliminated all spillage... https://a.co/d/007FwbcR As far as projectors go the 'lifestyle' projectors are absolutely a fantastic product with exceptional image, brightness and clarity. I owned many Epson products including their UB line 5030UB, 5040UB and 5050UB and I have not gone back to those for a reason. JMGO has their upcoming line in the N3 Ultimate that will have optical zoom, optical lens shift and Dolby Vision making it VERY hard to beat.
Just got the JMGO N3 Ultimate, I also had these three comparisons in mind because of the similar price range. However, best decision so far.

Valerion
VisionMaster Pro 2
Great picture/gaming, but RBE and no lens shift are dealbreakers.

Epson
Home Cinema 5050UB (V11H930020)
Great value with huge lens shift, but outdated lamp tech and poor HDR.
Epson
Pro Cinema LS12000 4K PRO-UHD Laser Projector
Superb 4K/120Hz gaming and no RBE, but requires calibration.

BenQ
W1070
Budget king, durable with good image, but RBE can be distracting.

BenQ
HT2060
Excellent 1080p contrast and quiet gaming, but low brightness for big screens.

Ranked #1
Valerion - VisionMaster Pro 2

Ranked #1
Epson - Home Cinema 5050UB (V11H930020)

Ranked #1
Hisense - Laser TV PX3-PRO

Ranked #1
Anker - NEBULA X1 4K Triple Laser Projector (D2351)

Ranked #1
BenQ - GV50 Portable Projector

Ranked #1
Anker - Mars 3 Air