What type of visa do I need to extend my stay in Thailand until January 15?

Simply extend at your nearest immigration office before the current stamps expiry date.

First with the "normal" 30 days.

After (if government still allows, we don't know yet*) apply for a 60day "Due to Covid" extension if you like to stay a tourist. All extensions cost same . . . 1900tbh

* Covid extension can be applied for till Sept 27, most likely they keep pushing this date forward as they (government) been doing since last year.

Presumably you're on a visa exempt for 45 days? In which case you can get one extension for 30 days.

After that you might be able to get an unable to travel due to covid extension but that will depend if they extend that or not, we won't know more on that for a month and a bit. If they extend it then that may take you through to Jan.

If they don't extend then it's going to come down to what exactly you're doing and what you plan on doing going forwards, as Stuart above says.

Depends on a number of factors. What age are you. Are you looking to work/study/volunteer etc?