Any light that falls, or reflects, on the screen will impact image quality.
You must eliminate any lights from falling directly on screen. This means that LED strips, open bulbs, etc. must be shielded from directly falling on the screen. Based on your request, this is a requirement, not an option.
The HD25 is cheap - period. It isn't the 'best', but it is a solid projector. The BenQ W1070, W1080, and Optoma 131 are all similar competitors to this model and will perform similarly.
All have plenty of brightness for a 92"-110" diagonal 16:9 screen.
You still want the best light control possible.
This is the key! If you do not properly control light in the room, then you will impact image quality directly. The less you control light, the worse it will look. Fortunately, these are all 'living room' projectors. They are brighter than a dedicated home theater projector is and they give up contrast and image processing in favor of additional lumens, so you should be good no matter what.
Your expectations really will be the determining factor as the 'best' is relevant to those viewing. I would expect pretty good results if you get good blackout curtains in the room. If you add some dark paint, you could get exceptional results with a standard white screen, or even a painted wall.