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.
Domain authority is an important ranking phenomenon in Google. Nobody knows exactly how Google calculates, ranks and rates the popularity, reputation, intent or trust of a website, outside of Google, but when I write about domain authority I am generally thinking of sites that are popular, reputable and trusted – all of which can be faked, of course.
to avoid throwing link equity away, you might create HIGH-LEVEL IN-DEPTH TOPIC PAGES on your site and redirect (or use canonical redirects) any related expired content that HAVE INCOMING BACKLINKS, to this topic page (and keep it updated, folding content from old pages, where relevant and there is traffic opportunity, to create TOPIC pages that are focused on the customer e.g. information pages)
QUOTE: “Starting April 21 (2015), we will be expanding our use of mobile-friendliness as a ranking signal. This change will affect mobile searches in all languages worldwide and will have a significant impact in our search results. Consequently, users will find it easier to get relevant, high-quality search results that are optimized for their devices”. GOOGLE
If a PARTICULAR CANONICAL HEAD KEYWORD is IMPORTANT (even perhaps a SYNONYM or LONG TAIL VARIANT) and I think a particular 301 REDIRECT has some positive impact on how Google judges the quality or relevance the page, I will make sure the CANONICAL HEAD KEYWORD and SYNONYMS are on the FINAL PAGE I redirect Google to (which is the one that will be rated and cached).
Write a description that would both inform and interest users if they saw your description meta tag as a snippet in a search result. While there's no minimal or maximal length for the text in a description meta tag, we recommend making sure that it's long enough to be fully shown in Search (note that users may see different sized snippets depending on how and where they search), and contains all the relevant information users would need to determine whether the page will be useful and relevant to them.
Another excellent guide is Google’s “Search Engine Optimization Starter Guide.” This is a free PDF download that covers basic tips that Google provides to its own employees on how to get listed. You’ll find it here. Also well worth checking out is Moz’s “Beginner’s Guide To SEO,” which you’ll find here, and the SEO Success Pyramid from Small Business Search Marketing.