I had the same dilemma a few months back & while nowhere near your level of scoring it was obvious for me to improve I needed to get off the starters. I strongly recommend you search the forums for scotthopes pro shop tables as that spreadsheet was a real time saver for me in being able to compare all of the clubs at a time & just filter out any I wasn't interested in.
My upgrade path was to get a driver first & I went with the level 81 Ping you mention. I liken the driver upgrade to a superhero first discovering they have super powers. It was a real game changer from the get go once I got used to the metre speed especially in CC tourneys from the back tees where sometimes the starter can't even get to the fairway from the tee.
I also upgraded my wedges at the same time, I started with just the one (I was doing surveys to build up credits). I started just taking notes on distance & number of times I was using wedges in a round over a few days to see which one I needed the most & purchased it. I went with the Max level 50 odd as they had the most spin & again were a game changer even while still on starter balls.
Next I went with a iron set but would recommend you get 3 (some people recommend 4) wedges first as my problem was by getting 1 wedges first & then irons I had a gap in low range distance as didn't realise / take into account the wedges that are part of the starter set & not separate clubs. It wasn't a massive issue as could still get around it by hitting lower percentage but getting the second wedge shortly after made a huge difference around the greens.
After that I looked at balls & went with the 10 Credit ones & noticed a difference in spin & control over the rocks. I then went to the 44 credits to see if the slower metre speed (1) made a difference, which it did & have now settled on the 64 credit ones as they have a slightly slower metre speed (2).
Good luck in whatever path you take.