Sum up the premiums on your insurance, as well as the maximum out-of-pocket expenses on that insurance, and you have a good estimate for your maximum medical expenses in a year; you should get a number that comfortably fits in a 31k budget. Insurance exists to make medical costs predictable and budgetable.
Hence why I said "good estimate" rather than "absolute maximum". However, the kinds of problems that health insurance won't buffer for you will generally screw you whether you have 31k/year or 131k/year.