In terms of cheap things to try, I'd like to recommend trying a nasal stent. I don't snore because I side sleep, but do if I'm on my back, and I suspected some minor apnea was taking place regardless of position. The stent has noticeably improved my sleep quality.
If it doesn't help, you're out twenty bucks, if it does it could literally add years to your life.
I've had good results with a nasal strip (like BreatheRight) plus an anti-snoring appliance (like zQuiet). I had a dentist-provided appliance that cost me $1000 out of pocket and broke in less than a year (when I had moved out of state); the zQuiet + nasal strip helps just as much and is an order of magnitude cheaper.
This happens to be the exact one I tried. I'll probably try others in case there's one which happens to work better or be more comfortable (irritation of the nostrils at first was a real factor, took about a week to adjust), but with a hydrogen peroxide bath every few days they can last an arbitrarily long amount of time, so I haven't felt the need.
If it doesn't help, you're out twenty bucks, if it does it could literally add years to your life.