There is no magic recipe to ranking higher on Google. I have had on-site training from Google on SEO, nothing is disclosed. All you can do is build the best site possible, however there are a few things that Google looks for.
The key to good SEO is quality content. I would recommend writing everything in your normal voice, while thinking about some of the keyword phrases you would like to rank for. Target your content towards these keywords without keyword stuffing, or typing anything that seems unnatural. Also, think about some of the geographic areas you want to rank for. It is typically best to have your primary geo (most likely the office's location) and 3-4 secondary geos mentioned throughout the site. You'll find that many searches will include a geo tag, example "Foot Doctor Honolulu". Check out Google Trends to get an idea of the search volume in your area. It doesn't really help to have the top spot on the search results page if no one is conducting searches for that phrase. I am not sure what the demand for Podiatry is in your area, but there may not be a lot of volume to begin with.
Your offsite strategy is also important. Focus on creating a few quality backlinks to your site through well known directories with good reputations. Do not just buy up backlinks- this is black hat and will hurt you, but having a solid directory on a site like yelp or yellowbook that links back to your site will definitely help.
I also echo the push towards SEO Moz. They have a ton of beginner articles that can be very helpful. I also know that you mentioned an aversion to running some paid search through Google Adwords. I would reconsider that if I were you. It will typically take at least 3 months before you are going to see major jumps in rankings. Running an Adwords campaign can help bring in traffic while you wait for Google to crawl your site. Run some test searches in your area to see if other offices are running campaigns. If not, the cost would be extremely low, and a small budget could have a major impact on your site performance. You could also limit yourself to just a couple of months until your organic traffic rises to a better level.
I hope this helps!