I figure if I charged $10-15 per house, I could easily make $20-30/hr -- About double the hourly rate of my current day job. I'm not a very outgoing guy, which is why I'm asking the internet for permission first :) Let me know what you think!
Most anyone who is going to say yes to $15 would have also said yes to $20. The hardest part is getting off of $0. Once you have someone off of $0, it's easier to move them to a higher number than you think.
Don't undercut yourself needlessly.
I think you need to target around $40/hour spent actually shoveling, so that you get to $20/hour overall.
Also, have a plan for variable amounts of snow. You don't want to get the same for 9" of heavy slush as 3" of popcorn snow.
We did this in my family when I was kid. Dad was a schoolteacher in MD (so we had the school day off anytime there was plowable snow). He'd go around in the plow truck and drop me off with the shovels for the sidewalks and spots the truck couldn't get. While I was shoveling different businesses on the route, he was driving around plowing. (Some jobs were more truck; others more shovel.) It was a pretty good gig for us, and I was able to convert several of the businesses to be my grass cutting customers as well during the summer. We found that we couldn't really bill people more for 6" of heavy snow than 6" of light snow. Customer mindset seemed to be "I'll pay more for higher snow; that's fair" but many couldn't wrap their head around 3" of heavy being harder than 8" of light, so we billed only on height and number of visits needed; if we had to go back twice, we'd charge 1x for the last visit and 0.5x for the others. For homeowners, that's usually not a factor, but businesses that wanted to stay open were often happy to pay more for a large storm if we could keep them operating. I think we billed a set amount for 3" and then an increment for every 3" above that, but it's been a very long time and you'll need to figure out for yourself anyway. For sidewalks and homeowners, you want a simple to understand and fair-sounding price model. Probably don't want to whip out any y = mx + b on them, but something simple and fair.
Your mindset isn't to convert every penny-pincher, but rather to convert the people who will value the convenience of not dealing with it. Those people are buying convenience, not cubic feet of snow removed or minutes of shoveling avoided. Price according to the value they get, not your costs/efforts.