Easiest to apply for non-o through local embassy. The London embassy certainly does not require a health insurance and neither does the extension in BKK. Non-OA however does require a health insurance as does the Non-OX i believe.
Financial requirements for Mexico’s temporary residency have increased hugely over last few years and regularisation programme has just been stopped. True, residency is very easy to obtain if you meet the “economic solvency”. Mexico is very different from Thailand though.