MIM Jazz basses are better than they've ever been and the FSR might be the best of the lot.
I own an MIM Jazz and an MIA Precision. I just scored the P yesterday (see NBD!

).
I am saddened by having to sell the J, believe me ($1,349 was a lot to pay up front...). If you score a decent MIM J, you will love it. There are some crap ones too, though. You can probably find the latter for anywhere between $200-400.
If you plan to use it sort of often and you can afford it, sure! Get the MIA. The Standards are amazing. Those CS60 pups are wonderful. The MIA Deluxe N3 (noiseless) pups were not so great. Love em on my new P bass!!! Buy brand new at just over $1300 or used between $800-$1200. Your call.
If you gotta save money, the MIM should do fine. Just make sure to buy local, because like I said - there are crap MIM basses out there. Some of my factors on buying a bass are
Quality
Is it worth what I'd be paying?
Feel
Is it ergonomically sound? Plays well?
Sound
It should sound nice.
Electronics
I need electronics suited to me.
Material
No cheap stuff that will break.
Profitability
Will it pay for itself? Or sit in my room forever?
Most of the standard buying factors... But it might help you.
Good luck and welcome to TalkBass!