Well, if it's just for your friend a private app may be the way to go. Public apps are the ones that require Oauth tokens to get access, but when you create the private app authentication details, the shared secret is basically your Oauth token (except the URL you must use includes the private apps username / password). Other than the authentication step, there's no difference between a private or public app.
I agree the docs are often sparse or sometimes just plain wrong. If it's just for your friend's store, I would manually create the links you need in the theme/templates editor in the shop admin rather than do it via an App, but both methods are possible. As I don't know exactly what kind of interface / workflow you want your app to have, I can't say if an application proxy (which I've never used) is the way to go.
Although there are a lot of Ruby examples, in the end all you need to worry about is the RESTful endpoints that Shopify provides. You simply make HTTP requests to them, and they will spit out a response, so the API itself is language agnostic. There are example applications in a few different languages including Ruby, Node.js, and PHP.
I hope that helps.