2 visa exempt stamp per year at land crossing, the sequence does not matter. And if you come in by air they have no legal limit. And coming in with a visa also does not count towards the TWO visa exempt per calendar year.
I think you may have worded it wrong, you can not stay 6 month without leaving the country. One entry is 60 days, than a 30 day extension. Than leave and come back to get another 60 days,,,,,,
you will get a 30day visa exempt stamp(correct wording) which can be extended by a further 30days at Immigration inside Thailand. As a first timer they usually not ask any addl documents, but they may ask the purpose of your stay.