I've worked for non-profits many times over, directed non-profits, freelanced through them, and started my own (and been audited multiple times as well) non-profit.
One of the biggest mistakes non-profits make is expecting quality results for free, through volunteers, who, while they may have hearts of gold, don't have the vested interest in an NPO's success that a paid employee does. I can't tell you how many volunteers for different non-profits I've met who are misused, love what they do but feel misunderstood by their Board.
But to address your question directly, if you already have an online presence, you've "jumped the gun." Because the developer you'd work with would have to probably restructure messaging, branding, with blogging, SEO, and everything that goes into successful promotion.
Personally, for $10 per hour, I wouldn't trust results, either, because that person would a) always be looking for a higher-paying position or work to augment that income and need to survive, and not be too excited about doing the work knowing they could go to a local fast food restaurant or day labor facility and make more and possibly get health benefits as well. Freelance sites post people who are desperate for work, and need money to buy food. That's why they accept work for lower-than-professional pay wages. It would be like me paying someone $10 to help promote my business...and then being surprised that we didn't garner satisfactory results. You get what you pay for in most cases. My dentist charges what he's worth, as does my mechanic, my CPA, our lawyer, and so on. Why would a professional work for minimum wage or close to that if they're any good?
I would suggest re-examining why the pay must be so low and expectations higher. If pay must be low, whatever you'd get back at ten bucks per hour would be a blessing. I would petition the Board for respectable, professional level wages, work with a local agency (which would obviously balk at $10 per hour), try to do it myself if necessary, wait until more funds are available and budgeted, or simply wait until more prepared to launch.
We once got a phone call from a local area woman stating she wanted to start her own non-profit helping other non-profits with their internet marketing. Since she herself didn't build sites or program or design, she wanted someone to build their company site with the promise to potentially refer future work. Her budget was $200 total for a professional online presence. She didn't know what SEO was, didn't care, didn't want eCommerce because she saw no need for it, wasn't interested in blogging because it was "too much" work. When we tried to advise her to raise her budget for better quality results she simply hung up. Needless to say, her non-profit never launched successfully.
Give more to get more, expect more in return.
Best of luck to you.