Hi Carl,
The fluctuations in ranking are quite normal. Think of Google as an automated "learning" machine. Your site is pretty new, so is probably not getting that much visitors. By playing with the rankings, you will be able to get a little bit more traffic, generating additional data, which Google can than use again to see how your site is performing compared to the competition in terms of visitor engagement.
However, this is only one of the many factors involved, incoming links, number of articles,... etc all play a role (an exhaustive list can be found here).
Unfortunately, while being at number 51 with one post with no shares & links, doesn't guarantee a number 1 position if you add the shares & the links. Patience is a virtue you definitely will need to have if you're doing SEO.
Given the limited experience you have, I think you'll have quite a challenge by taking on your first client. I imagine that you already read the Moz Beginners Guide to SEO (http://moz.com/beginners-guide-to-seo). There are some very good articles on SEO audit on Moz as well (here and here) and plenty of resources on keyword research (http://moz.com/beginners-guide-to-seo/keyword-research for starters).
Be honest with your first "customer", and make it clear to him that this will also be part of your personal learning process. SEO is not an exact science, and the basics are quite easy to learn, but as these basic techniques are known by everyone in the business, you're not going to make a huge difference by only applying these rules.
Most important rule in SEO for me would be - Imagine the different kind of visitors/customers you would like to attract. Put yourself in their position, and think about how you could deliver them the best experience possible on your site. If you are able to make your visitors happy, and you succeed in making them happier than your competitors can (by having excellent content, great products, fine usability,...etc), you are on the right track.
Dirk