How about showing some examples of the music?
Since chamber music isn't full of loud crescendos and extremes of the type heard in rock & full orchestra, I think I would recommend against using a sub, in favor of finding the best speakers you can in your budget. Tiny bookshelf models aren't going to give you what I believe you're looking for.
My room was roughly 11' x 16' until I took out most of a wall, removed a closet and moved the entry door back about 4'. Now, it opens to the kitchen and doesn't sound like a small room. In my case, I got really tired of throbbing bass while I still worked in car audio and, while I used a sub for years, it was because the room and my speakers didn't do a great job on bass. I eventually became so dissatisfied that I build a pair of speakers using WinISD and one of the members here sent a crossover design for them, using BassBoxPro. I haven't felt the need for a sub since and it has been around 5 years. They go to the upper/mid 30Hz range before the low end drops out and since most of what people think is deep bass is really the second octave (40Hz and up), these do very well for a wide range of music, including classical. Is it like a true full-range system that digs into the 20Hz and under frequencies? No, but it sounds great for music and special effects in TV and movies- surprisingly well, actually.
I think that it will be easier to achieve a convincing sonic image with a good 2-1/2 way using 6-1/2" woofers than trying to get a sub and satellites to work together seamlessly. In my room, when something is supposed to come from the center, it comes from dead center and it's rare that anything sounds like it's just coming out of a speaker. They can be a bit light on bass at times, but mostly, that's because of the recording and some things are again, surprising in the level of the low frequencies.
You may be able to find something at one of the local stores that was returned- as long as they make sure the equipment performs to spec, it's not a bad way to experiment and find out what works, or not. I found a set of Polk T50 towers that were returned, but I don't know where you are, so it's hard to recommend where to go for these. I found a very complimentary review of these and unless you also listen to EDM, pipe organ or anything with extremely strong and deep bass, they might work.
