Just a quick stats glance has me leaning towards the wedges for you for a few reasons:
- 17 foot average distance to the pin
- 2.27% on putts 10-25 feet from the hole
- 64.65% greens in regulation
If you're not getting to the green in regulation 35% of the time, that means you're probably hitting a lot of short shots into the green. You're averaging 17 feet from the pin, but only hitting 2.27% of your putts for that range.
Better control into the green is going to bring the number of putts down because you're getting closer to the pin. Your average putts per hole is pretty good at 1.7 (mine is exactly the same - room for improvement, but a good start).
Someone mentioned before that the Starter wedges are horrible and I agree with that. The starter putter isn't that bad. When I was in your place, I bought the putter first. If I had it to do over, I would have gone wedges first because when I did get some better wedges my scores got dramatically better.
That all said, though - go with what you feel like your the "worst" at using - do you feel like you putt well? Do you feel like you have good control over your short game? Whichever one you answer "no" to more strongly, go with that.