I hope this helps! Please don’t be discouraged by editor’s rates. Many of them do this full time or to supplement their other income with their business. The quality of service is not necessarily tied to project cost, but hiring anyone who is a contractor or freelancer often means you’re getting one-on-one personalized attention you might not get if you worked with, say, just the editor of a publisher who could see your book as a quota to fill. Just my two cents!
Moreover, the casual distinction between a (developmental) “editor” and a “copyeditor” can be a bit simplistic, particularly in a self-publication or even vanity-publishing context. A self-published author may barely have the budget to hire one editor, so that editor needs to be able and willing to blur the lines between developmental editing and copyediting. The editor must also be accustomed to working with authors of a variety of strengths and weaknesses, including many whose work would not, in fact, have been accepted by a commercial publishing house in its current form. I have come to take great satisfaction in taking a new or newish author by the hand and helping them find ways of making their work the best it can be. Of necessity, this must include line-by-line correction of grammar and style (often a surprisingly great amount of such correction), but can rarely be limited to that.
When you’ve found someone who seems like a decent candidate so far, make first contact. (The contact form on the website is fine as a first step.) Introduce yourself and state what you are looking for (a developmental critique, copyediting, etc.). Give a very brief description of your project, including its genre and approximate length. Give an idea of your planned next step and any deadlines (even if only approximate ones). For example, have you already signed a contract with a subsidy press for publication next fall? Are you planning to submit the manuscript to publishers and/or literary agents after editing?
That’s a great point about other disciplines. Why should writing require some outside arbiter? Is it because these other disciplines consist in crafts that require significant training, whereas anyone who’s literate can start writing a book at any time (and therefore, the threshold for entering the medium is much lower)? I do hope you’re right about learning self-editing skills. I actually just made a YouTube video about how to self-edit: https://www.youtube.com/watch?v=3mmLEuH9x28