Putting mats are good for working on your stroke. Put a line on your ball and try to hit it straight. They don't help you with speed or the ability to read a green. I have yet to find a putting mat that plays at the same speed as a real green. I have a birdie ball put up mat and that is better at simulating a real green because it has that wedge that slows the putt. Plus, how often do you get a flat putt?
I have 3 launch monitors: a PRGR, a SC200 and a Skytrak. The Skytrak was heinously expensive, relatively speaking, but it's awesome. The other two are ok, especially if you are hitting on a range. But if you are hitting into a net, you won't get feedback on how far offline you are hitting. I have a net and mat set up in my garage. With the Skytrak, I can pop out to the garage for an hour and work on my swing. It would take me that long just to drive back and forth to the nearest driving range.
Lessons are great, but a couple hundred dollars isn't going to get a lot of instruction. For the cost of the Skytrak, you could get some meaningful instruction but you still need to put in the time outside the lesson to make anything learned stick.
Spending the money on more golf would be fun and would make a great birthday present, especially if you play at a bucket-list course. My 60th b-day is in a couple of weeks and that's what I'm going to do.
Anyway, my vote went to the launch monitor.