Tough choice in that room. Having wall mounted speakers might work in the far corner but not so great next to the doorway. In our living room I opted to mount the surrounds up high in the rear corners, so higher than what WIlliam has sketched in the photo. High surrounds are not ideal but they still make an audible difference if you just want to add some effects to movies. If this is primarily a music setup I would stick to 3.1.
As to how I would go about it in that room, I would get speakers with mounting brackets and just run cables on the floor to test things out. 14 gauge stranded copper is not that expensive. In that scenario, if you don't like the result, then you only have to patch a few screw holes and touch up the paint. If you like the result, then the trick is hiding the wires. Only a couple options that I see since you can't go in the ceiling. If there is basement access, then down from the stereo, through the floor joists and up the walls. If no floor access, then either in-wall or surface mounted. In-wall will require a lot of patching and repainting. For surface mounting you can buy tracks to run the wire inside and run the tracks on top of the base board. The lack of trim around the doorway will make that a tricky option as well.
As to speakers, depends on your budget. I am planning to replace my surrounds with the
True Mini from Philharmonic Audio. You'll be hard pressed to beat the sound in that size but they are $380 US + shipping. They do make them in white, though, which I'm sure from the photos is your preferred colour.