What type of visa should a UK citizen apply for to stay in Thailand while getting married?

well seeing as you're NOT married to a thai right now, and won't be when you enter thailand I'd say get a single entry tourist visa from the Thai consulate in London using the eVisa online system.

The visa will be valid for 3 months from the date of issue <- meaning you have 3 months to ENTER thailand on it and get stamped in for 60 days, AND you can extend that once for 30 days when you're here at the immigration office for 1900baht

In total that gives you 90 days to GET married 😛 then you could apply for one 60 day visit thai family extension at the immigration office based on marriage to a thai for another 1900baht and that'd give you a total of almost 5 months in country