Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.
Google is a link-based search engine. Google doesn’t need content to rank pages but it needs content to give to users. Google needs to find content and it finds content by following links just like you do when clicking on a link. So you need first to make sure you tell the world about your site so other sites link to yours. Don’t worry about reciprocating to more powerful sites or even real sites – I think this adds to your domain authority – which is better to have than ranking for just a few narrow key terms.
Thank you for the great checklist. It is really useful and gave us a couple of new hints on optimization process. We’ve been using WebSite Auditor and found it exremely helpful in site’s structure and content analysis, bringing all the statistical information on the validation errors, social mentions, duplicate stuff, etc. under one roof. Still there is so many different SEO information you sometimes cannot understand what to start with. Fortunately you answered this question. Thank you again!