12 X 16 playhouse; 6' feet above ground
Deck design is typically regulated by some sort of code, in my town we operate under the 2006 International Residential Code. There is really no debate about how to build decks in my town, the building inspector gives you a copy of the Prescriptive Residential Wood Deck Construction Guide, you follow it, he approves your plan, and approves your construction. Or you don't follow it, and either you get an engineer to design all of the aspects that do not follow the book, or you don't get a permit.
You may not need a permit for what you are building, and if you do, it may not follow deck design standards, but it would be a good idea to follow a standard design and construction procedure such as the Prescriptive Guide, unless you plan to either engineer the playhouse yourself, or get it engineered. A 12 ft x 16 ft playhouse is pretty big, and at that height above ground, you really should think carefully about construction practices. You asked specifically about setting the post bases, which is covered in glorious detail in the Prescriptive Guide. In the Guide, the size and depth of the required footing is specified (this is a concrete footing), and the means of attaching the post to the footing is specified (you need to use a galvanized steel standoff bracket, you are not allowed to bury the post in the concrete).
Now there are folks on here who probably think I am one level above or below being a communist for suggesting that you follow code, but even if there WERE NO CODE in your area, I would still suggest following the guidelines in the Prescriptive Guide, since it will give you a conservative design likely to last a long time, and will go a long ways towards minimizing the chances of someone falling off the deck or going through and getting hurt. Posts are just one of many design details covered in the Guidelines, which are free and can be found on the internet. Course your town may have different requirements, always good to check first with your building inspector.