I'd head on over to the Speakers forum to seek help on the latest offerings in budget/bang for the buck speakers.
You have a decent size room there. Go take a look at the subwoofers forum to get a handle on that department. But I'll tell you, it's pretty much agreed upon there that when you can get it on sale @ Newegg (which they have frequently for around $280 w/ free shipping), The Klipsch RW-12d is probably the route to go for budget subs.
I have it and can attest to it being awesome!
Regarding the AVR, do you have a brand preference? Is there certain features you need/want?
There's a lot out there that can be had cheap. Especially that the new models are coming out and last years are on sale to clear inventory. Also, don't disregard the refurbs as you've been looking into already. They have some killer deals on them from time to time.
Matrixed is when they take the sound track and add to it by interpreting what might be somewhere based on whats going on.
There's many implementations to get to 7.1 for only 5.1 audio soundtracks.
Then to go 9.1 or 11.1 you have to options
Dobly uses it to add front height. So only up to 7.1 or 9.1.
DTS uses NEO X to add either front height or front wides.
Some AVR's have both or just one of those. But I think now a days, all can matrix 5.1 to 7.1.
Your room is kinda narrow so if you ever get to adding that many speakers, front height might be better for you. But you may decide that only 5.1 is ok and better for you based on your budget. By adding a few at a time you can play with it and see what you like and works best for you.
You should read up on surround sound.
Initially, you will have to go over your $500 budget to get a good start. But I guarantee you, in the long run you won't be disappointed.
Too many times people skimp on the audio and focus on video but they fail to realize that speaker and sub technology doesn't change as rapidly as the video side does.
What you get for speakers (if done right the first time) will long outlast whatever you have for video. Speakers/subs (and AVR's to a certain extent) are some of the least changed out parts of the home theater system.
I started out w/ different variations of HTiB's over the years and gradually went up to separates using a 6.1 Polk Audio system then a 7.2 Yamaha system. I even for a very small time had the Klipsch THX Ultra2 system but had to sell it.
You really appreciate better sounding systems over time.
I think HTiB are better for a more non dedicated space or people who are on a budget and that budget will never increase.
You have a dedicated room and projector setup, compliment it with separates and have a real home cinema experience.