A projector throws light; what that light lands on decides how much of the picture you keep. Plenty of people start with a plain white wall, and for a first try that is a sensible move. The question is what you give up, and in which room.
In a properly dark room, a flat, matte-white wall and a basic screen sit closer together than the shop pages suggest. Switch on a lamp, or watch before sunset, and the gap opens: room light lands on the surface just as the projector's light does, and it lifts the darkest parts of the picture towards grey. A screen is flat and has a known, neutral white. An ambient-light-rejecting (ALR) screen goes further and is built to favour the projector's light over the room's.
Pick a room and a surface. The panel shows what happens to a dark, moody scene. It is an illustration of the effect, not a measurement of any product.
A dark room, a smaller picture, a rental flat, or a trial run to find out how big you want the image to be. Use flat matte-white paint if you can.
If you watch only after dark, your wall is smooth and you are happy with it, wait. If the room is never fully dark, the picture is large, or you have noticed a colour cast, a screen is the cheaper upgrade than a brighter projector. Matte-white or ALR depends on how dark you can make the room; if you can make it dark, matte white is the sensible default.
The picks below are conventional matte-white screens, from a compact 84-inch to a motorised 106-inch; none is an ALR model. Check your projector's throw type and the width of your wall first. Prices change: expect roughly €150–200 at the low end and €900–1,000 at the top.