I believe the ideal first purchase would be the Spider putter. (The Redwood putter is a lot better, but it's only available for the Pro+ tier.)
The second thing to buy is a driver, and I would recommend the Rapture 10.5° driver. (Again, the Rapture Pro 9.5° driver is a lot better, but it's only available for the Pro+ tier.)
I'd also recommend using advanced ball types. The most expensive ball types are the most useful, naturally. I would recommend GI-SD balls or GI2-S balls. (The first of these is only available for the Pro+ tier.)
But, you can also advance to the Pro tier using the basic free equipment set. It will just be more difficult, and I'd say also less fun.