What visa should an Indonesian citizen married to a Thai spouse apply for to stay long in Thailand, and what documents are needed?

first off you'd need to bank 400K baht in a thai bank account in your name only to qualify for a Non-O visa based on marriage to a thai.

You also need a minimum number of days left on your current entry stamp (most offices are 15 days or more some are 21) so you can apply for the Non-O visa inside the country at the immigration office where you live

As far as documents you and your thai wife need to go to your immigration office (there are over 80 offices in the country) and get the hand out from that office listing the requirements to apply for the in country Non-O visa based on marriage..

You could also get one 60 day "visit thai family" extension which can buy you time on your current stamp to get the proof of funds and the other documents together so you can apply for the in country 90 day Non-O visa