Well SEO for mobile site starts with having a proper mobile template in place - a good one would address all the basic seo needs already and there's very little that you should worry after installing/running the mobile template respectively.
Another major aspect of the mobile site would be implementing AMP - this is the latest gig by G in which they have promised sites with AMP running would have advantages (not that I am seeing), but since that's what G is saying, you should definitely take AMP very seriously.
Once AMP is installed, the AMP page would be cached on G, and when someone opens your page, they will access the AMP cache first which has a very fast loading speeds, which the speed would be a bonus for your site in that aspect.