What type of visa do I need to stay in Thailand for 5 to 6 months on holiday?

That is best done with regular tourist visas. Get one upfront, extend, plan a trip to a nearby country after 85ish days, get a new tourist visa there in addition to the sightseeing activities, and if you stick with 5 months you're then set, otherwise you can extend and reach 6.

As an alternative, you could just hop across a border when the first 90 days run out, get 30 days coming back, and extend those. That'll get you to 5 months as well, but going beyond requires a second trip to a border.