Well, I've been a Jazzmaster owner since 1994 or so. I have a made in Japan model since then, but I own an American Vintage reissue since recently. I rebuilt my Japanese made model, all new everything except the body and neck (and tremolo).
I can tell you that the Jazzmaster, in my opinion, is the best guitar ever made.
But they take some work and getting used to.
1) The pickups aren't P90s and don't sound anywhere near the same. P90s have a grind and a honk to them that Jazzmaster pickups don't have. That being said, most things that go by the name "Jazzmaster" don't have Jazzmaster pickups either... the MIJ model that I have came with what is basically considered Strat pickpups in a Jazzmaster body. I have since replaced them with handwound pickups.
2) My favorite thing about the Jazzmaster is that Fender old school neck, with the round 7.25" radius. American Vintage models have that also. Not everyone likes that as much as I do, so the newer models have the current 9.5" radius. That's up to you, really. No wrong or right either way, only opinion.
3) They only feed back if they aren't properly shielded. Chances are, yours won't be, or if at all, not very well. The feedback is actually very cool, as has been noted... but I still shielded mine properly. You can read about it here:
By the way, that is the best site to learn about Jazzmasters, no offense to this wonderful forum.
4) The string will pop out of the grooves, more so on Japanese made Jazzmasters than AVRI ones. Honestly, you get kind of used to it... as well as the other things you have to do with a Jazzmaster. I dealt with it for so long that it came as a surprise when I realized that most guitarists don't have to do any of that. There are a lot of alternatives, though, the easiest of which is the Mustang bridge, which I have on my AVRI. My Japanese made one has a Mastery bridge, which is in the Nels Cline video below, but is very expensive.
5) The tremolo is what it is... I can't comment much since I don't use it or any other tremolo. It is its own design, and it's not bad. But it's not like what a Strat has or what a Bigsby is or anything. You'll have to get to know it, and I bet you'll find some use for it. But there isn't anything else like it, so don't be expecting anything like what you've known.
6) It is the best guitar ever.
I know folks are going to jump on me on this site... and I freely admit that the Telecaster is the second
best guitar ever. But there is a lot of extra string on the Jazzmaster behind the bridge. It's not just sitting there, it's alive and resonant, and it makes the whole guitar both of those things as well. You can strum it, and get these ghostly sounds out of it. Your amp will react in unpredictable ways, and if you like feedback... you get it in a heartbeat with that. But even if you don't do that, those strings are vibrating and putting out harmonics like you wouldn't believe. The downside is, this design doesn't lead to much sustain... the Jazzmaster is rightfully criticized for not having much of that. You can get a Buzz Stop, which increased the break angle and is said to add sustain. I bet it does. But I would never want to give up the magic that a Jazzmaster has simply to get more sustain. I'd rather just buy a Les Paul if I really need sustain.
Now, I'm not knowledgeable about the Modern Players and the Blacktop ones are not really worth considering, in my opinion. The Classic Players look pretty cool, on the other hand, though... they all seem to be Jazzmasters for people that don't like what a Jazzmaster actually is. So take all my advice with a grain of salt.
Anyway, you either will or won't like the song, but this will show you what a Jazzmaster is capable of, anyway:
I say jump in! But then, I guess I would, wouldn't I?