Do not....I repeat...do not get a speaker that is too large!
Or you will be pummeled to death by the bass.
I have been down this road.
Your room is small, and a small speaker should load it nicely.
You are in a classic nearfield listening situation.
I would go with either a monitor or a small and simple floor standing two way. This gives you great flexibility in that if it works, fine, you are done. And if you buy used, there are many good options that would keep you well below your budget. If you find the bass lacking, you can always add a sub at a later date.
As I said in your other thread, I use Spendor S6 in a 10x11x8 room.
For sheer musicality, emotion and connection to the music, this is a good way to go. I started out teaming it with a REL Storm, but ulitmately found the bass fine without the sub, so I sold it.
The S6 has been replaced by the S6e so you can get it used for about $700-$750. A used REL Strata can be had for about the same, so you would be w/in your total budget. I'm sure there are many other candidates that would work just as well. I'm not pushing this setup specifically. Just providing an example of what might work well for your situation and your budget. In your situation, I think it is best to start small, see how it works, and then get big if you need to, by adding a sub.
I'm sure the monitor under consideration is fine.
Don't know if the RAW would be too big and overload the room.