Everything I need to know before buying projector that would be used mainly to watch Anime?

Hello guys, for few months I was thinking about buying TV and use it as my second monitor to watch Anime and rarely movie/TV show from my bed. But because of my room structure it's harder than I thought to find a place to fit it in so I was thinking about projector as substitute. Can you tell my in what price range should I search for projectors? Is picture quality as good as TV? Can I connect it to my pc easily and then stream the video and audio through discord? Do I need to repaint my wall in specific colour if yes what colour? Can I mount that projector on roof wall? Is it easy to adjust size of the screen and what size is best for it?