No, that is not a good first car unless you have deep pockets.
Aftermarket mods for the JK Wranglers are expensive, insurance will likely be very, very expensive (especially at only 16), and being that it has over 200k miles, that also means it's going to be due for some major maintenance. Typically transmissions tend to need rebuilding around that mileage.
I should also mention that the 2007-2011 Wranglers are known for having the severely underpowered 3.8 minivan engine in them, and they are notorious for burning oil. The 2012+ models are much better with the newer Pentastar engine.
Anyways, it's ultimately your call, but I don't think I'd recommend a high mileage, early model JK as a first vehicle.
An older TJ (97-06) with 100k miles or less would be a better bet IMHO, but you're going to be hard pressed to find a nice TJ with under 100k miles and no rust for $7300.
To be quite frank, I don't think you will find a good Wrangler for that price, unless it's a YJ possibly, but those are hard to come by in good shape.