Do you have free reign to treat the room how you like and can you paint a screen straight onto the wall?
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For what it's worth I've had a bunch of pj setups - home made screens with purchased fabrics, specialized paint and diy Black Widow, to budget and high end exotic fixeds and drop downs. High gain, neutral gain, various shades of grey. There's so many options it gets super confusing! Given this and if you can treat the room and paint straight onto the wall, this is my suggestion. Sand the screen wall down - don't have to spend ages but the more you do the better the result - and paint a massive 16:9 Dulux Lumitec Light and Space White screen. Go for as big as the wall/pj will allow given the room setup (this first part I suggest to anyone considering a fixed screen pj setup btw). Now paint everything else matte black. Doesn't have to be black, but it will look better the darker it is. This last bit will make a cheap pj look as good as one costing considerably more. Personally, i'd also buy some decent, non sheen black velvet - devore - staple it onto foam boards and velcro it to the walls and ceiling. Again, doesn't have to be the whole lot - but treating the screen wall along with the ceiling and side walls coming out a few meters makes a big difference. And it looks ******* smart as hell
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Ofc, black carpet - or failing that, black rug/carpet coming out a few meters from the screen wall. Your screen suddenly becomes what looks like a 100"+ plasma floating in space. Very few people have experienced this as it's not something you get at the cinema due to the low lighting and exit signs everywhere, and it looks amazing. In fact it can make you feel weirdly disembodied. All of this will set you back a few days work and a few hundred quid and will look better than a £2000 fixed screen in your average home cinema room. Now blow the rest of the budget on the best possible low contrast pj you can afford (i'm assuming the sound side of things is sorted?). JVC is usually the easy choice. If gaming is a concern, probably a Sony. But there's a whole load of pjs around - I like Epson too - so do some research. Also, get some black tape to cover the leds on your av equipment - don't want to go through the hassle and have evil little lights all over the place. Burkas are an option. And now you're good to go - it will already look fantastic. Better than the cinema and anything you'll get with a traditional panel. And this is where the fun really starts - play with image size for a few weeks/months and see what works best for your seating position/eyes. Be wowed by it. If you decide the sweet spot is a little smaller, paint in the new border and live with it for a while longer. Mess around with pj settings. Dabble in calibrating it. The screen can totally wait. In fact, buying a fixed screen and a pj at the same time is the biggest mistake, imho, that you can make. I made it, everyone makes it. Once you're settled and know what you want size wise, start saving for a screen. DIY or bought - things will looks crisper and colours more accurate, but it will have less impact on how good things looks than the stuff mentioned above. This may all sound like hassle, but it's the difference between walking into a room with a big tv and being in space watching movies through a massive floating window!