There is no easy way to stay 6 months as a tourist without leaving just once.
Best is a 6 months multiple entry tourist visa. Gives you 60 days each entry which can be extended by 30 days each time. So you have to leave and come back at least once.
You can get as many single re-entry permits as you want. The downside is it takes a lot of space in your passport and if more than 3 single re-entry permits a multiple re-entry would have been cheaper.
I often take a multiple re-entry permit for the conveniance.
baht must be certified by your national embassy in Thailand. Some countries do not give a income statement such as USA, UK etc. Then only 800.000 baht on a Thai bank will be accepted.