Between October 1st and March 30th, you'll get visa exempt entry of 45 days (it's simply an exempt entry and it's not any type of visa). And, yes, you can extend for another 30 days at CM Immigration for 1,900 baht and some paperwork. Would recommend going for your 30-day extension 10+ days before your 45-day exempt time expires just in case you run into a paperwork problem (not likely but it could happen).
Mae Sai border is not currently open for farang but, then again, you certainly don't need to do a border run if you're only staying 60 days.