Indeed best to get a tourist visa so you won’t have any hassle with going to immigration office and it’s almost half price from the extension. You can buy a cheap flight out after 60 days, a refundable ticket that you cancel or use
What you talk about is a visa exemption, not a tourist visa. The process is correct though. A tourist visa is 60 days, you have to apply for it at an embassy or consulate beforehand and you can extend it for 30 more days as well.