You need to get a reentry in phuket immigration office so that your non o visa will be valid when you return. Your 90 days will start when you come back
Check first if your passport/country is included in the free visa upon arrival... if included then all you need is vax certificate. Buy ticket and come to Thailand.
If not included in visa upon artival then go to a Thai embassy whetever you are and apply for a tourist visa..Apply personally. Not online