Just my humble 2 cents as a business owner about what you selected , it should work fine and it will sound better than you thought it would. I'm no audio expert by any means but I setup the sound system in my last store and it sounded great, in fact, it sounded better than or at least as good as any other restaurants/stores in town including national chains. For background music on a budget all you need is a decently powered receiver that can receive the sources you need, lower to mid-level speakers and a speaker selector that can supply them.
That said, I think the reason my store sounded so good was because I went overkill on the number of cheap speakers. The part of the store that had sound was basically a box. It had 12 ft suspended ceilings that was approx. 1100 to 1220 sq ft. and partially seperated by one wall. I put 6 pairs of 80w (maybe 60w, can't remember) speakers in the ceiling because I lucked out and found them as a close-out, discontinued deal for cheap. It really depends on the layout of your salon and how many walls you have but you cannot go wrong with more speakers for background music in my opinion. I suggest 8" because they sound a bit fuller than 6"even for lower volume background music.
For soft, background music for your salon, I say spend more money on extra speakers rather than worrying about things the guage of speaker wire. 16 Awg should be fine. If you were using the speakers in a HT environment I would suggest differently. In my new house I used 16Awg for my whole house system with a cheap Sima speaker selector and it rocks better than the NUVO system that I had in my last house which cost about 3 times as much. You can also probably go with less than 60-80w speakers, someone else from this forum would need to verify that since I'm no expert. Hope this helps and good luck with your business!