As you point out, with a $10/month budget, you're asking for quite a bit.
The only DIY site I would recommend for that is squarespace.com ($8/prepay, $10/monthly). Their sites are as close to valid code as I've seen, and actually quite cleanly written, mobile-friendly, SEO-friendly, the admin isn't difficult, it's hosted on Amazon's Web Services (last I knew), and the designs are nice.
With any site, the "lots of traffic" aspect comes down to your effort levels:
- Create well-written, descriptive content.
- Do the usual Google+/Yahoo/Bing Local pages, point them to your site.
- Register for Google and Bing's respective Webmaster tools.
- Download Google's Starter Guide
- Make sure your business name/address/phone (NAP) are the same across all fronts.
- Learn what you can and ask questions when you feel the need.