Candice
It sounds like your site is ranking as it is. The first principle is always do no harm. If you clearly identify a spam link - then disavow. But you are through the big updates and it sounds like the links have an organic origin - so not high from the information on the priority list.
Obtaining backlinks - require some strategic considerations. I will suggest a few easy options. Check out your link profile and see what links you can change from nofollow to follow. Might be just a phone call or two. But most importantly i would have a staff meeting - pay for the pizza... then explain backlinks to all the staff & make the staff part of the solution as well. Demand the boss get some editorial on the business and a backlink!
You cannot do everything - share the load.
Michael has identified page speed. That is correct - a big one, aim for under 2 seconds.
Hope that assists.