I literally just googled "wall mount bookshelf speakers."
https://www.amazon.com/WALI-Clamping-Bookshelf-Surrounding-SWM201/dp/B01GUITK24
By surround I was referring to side, as it is my understanding that in a 5.1 setup they should go to the side. The main listening position is the grey couch across from the TV, so figured I needed to get them to the left and right of that couch as much as possible.
My plan for the RP150M's was to either 1) Put them on stands to the left and right of the media center OR 2) Mount them on the wall using something like this. We are expecting to start a family soon, so having them on speaker stands could be a hazard, so I'd rather mount them on the wall if that does not take away from the quality too much.
Yeah, I would place the front speakers on the platform. Technically, it is a couple inches taller than is ideal, but KEF's coaxial drivers have excellent off-axis dispersion.
And you typically get more for your money with bookshelf speakers than towers, so it's the way to go for maximizing your budget.
There's really no good way of giving generalized advice for subwoofer placement. The ideal situation would be to buy a calibrated mic like the UMIK-1 and run sweeps in REW from multiple positions in the room, but that's not practical for most people.
Or the subwoofer position might just be determined for you based on foot traffic restrictions in the room.
In the absense of any other info, I would just try out the front right and front left corner of the room and see which one you subjectively prefer.
For the surrounds, you can either put them on speaker stands or get wall mounts like this one:
https://www.amazon.com/WALI-Clamping-Bookshelf-Surrounding-SWM201/dp/B01GUITK24/
Speakers and all is tough. I wouldn't honestly recommend built in speakers or placing your TT on a speaker.
If you can, mount some brackets on the wall at the appropriate height and put some 1280s up as Sharkamino suggested.
Even better would be if you could make some space for something like the Klipsch R-51PM (open box but blemished cabs ebay in wisconsin for 199) or R-41PM (new unopened ebay in texas for 239) that have their own preamp, then you wouldn't need to worry about it if/when you upgrade your TT. Yes they cost more than the refurbed Edifier, but they are more speaker
Given your space, though, wall brackets are probably the way to go. Or stands, can you put stands in behind the cabinet?