There are definitely a lot of strategies out there. The most "efficient" (and probably least fun) is to save your Credits until you get to some of the higher tiers and can get equipment that won't need to be upgraded as frequently as some of the lower tiers. [There's some sweet Drivers in the L70s, Vokey wedges in the upper L70s, etc.]
If you're mostly looking to increase the fun factor, Driver is where I think most players start. I was getting incredibly frustrated with the short game aspect and picked up a 64-degree wedge that instantly started shaving strokes off my game because I could knock it close inside of 50 yds. Same with putter: hated that the lower end putters could never hold a line.
Whatever you do decide: know that your trade-in value is 25% of the price you paid so you'll want to pick equipment that you're good to hold on to.