Yes There is a Market in Sarigerme, Market day is on Sundays. Starts at 9am and finishes at 5pm. Totally purpose build touristic market.
Stall owners can be pushy, annoying and rude most of times. Majority of the stall owners of sarigerme market are originally not from sarigerme village, they come from different areas of the region.
When it comes to markets , they are all same as same sales people moving around. from one town to another, therefore don’t think you would be better off visiting a different market then the other.
However, Fethiye market which takes place on Tuesdays seems the biggest one. Probably the best market would be the Friday Market in Ortaca Town, as this market is more local customer orientated and has more oriental essences especially with its prices.