Wants to spend a maximum of 150 euro, wants to hang it up on the ceiling. I have no idea how it works, but I definitely have to connect it to my Xbox or PlayStation and, if possible, to my cell phone or smart tv. Know me badly with projectors so Ka whether that's asking too much for the price
150 euro? I paid 4000 for a good one back then and it was reduced because it was an exhibit.
So… Um… Yeah… You don't get anything good for the price. There are some, but the resolution is 480p. It should be full HD these days and there's nothing for less than 180 euro. And I wouldn't take the cheapest either, because the picture is usually bad and they are too loud.
With some of them you have a high input lag, so you can't play with that. I once had one of those, believe me, that wasn't possible.
Projectors are only a niche product these days. The big problem with all beamers is the system-related low contrast / black level, especially in less than ideal environments. The fact is that the white screen is the deepest black that a projector can theoretically display.
In most areas, LCD displays are therefore the better option.
For 150 euro you can only get a toy projector, that's a lot of money. These have a very low resolution and very low brightness.