Best type of foundation is some what subjective. What are your goals? permanent? warm? easy maintenance? easy to work on? Keeps out bugs? easy access?
"Spa Observatory" Sounds to me like a much more than an observatory? Is the spa on the bottom level? Built in, or attached?
Is 15×15 big enough or are their ordances to be contended with? (When we built our screened porch, it started as a 12×12, then ended up with 14×18 and wishing we'd added 2 more feet.