@Paul **********
just come in as a tourist. As mentioned above you get 60 days when you enter Thailand on your American passport without needing a visa. And this can be extended once for another 30 days.
If you think about staying a bit longer, then apply for the Tourist Visa Multiple Entry. This visa is valid for 6 months and gives you 60 days each time you enter Thailand within those 6 months.
This will give you plenty of time to get to know that person and decide if you want to go to the next step. There is no need for another visum yet.