I agree that you really should try before you buy.
I can't lie, though, a guitar immediately sprung to mind: The Godin LG. It's not much on the "Jazzy" side, to be honest (though, Alex Skolnik played some jazz with an Ibanez shreddy guitar!) but it's a rock and blues workhorse that could be used for occasional jazz.
There are HB and P-90 flavours. I like the P-90s, but I can't stand the hum of single coils anymore. If you have a relatively quiety environment (you're not near a cellular network node and so forth) you could get away with the P90s. Otherwise, the HB model should do just fine.
It's not a guitar to everyone's liking, though. The neck is medium (not slim), and the body shape is an aquired taste (I love it now, but not at first!). But the worksmanship is superb in that price range.
Some of the PRS SE models look compelling, too. Again, not so much for the jazz, though they have a new thinline model that apparently apes jazz tones fairly convincingly.
If you're MORE into jazz and the blues and rock will be the music "on the side", the artcore recommendation is one to really pay attention to.
Final note: if you're just learning, anything with 6 strings will do, really. For your first guitar, you shouldn't be after "the tone holy grail" that will cover every musical style ever. You should just be after something that's inspiring and comfortable to play at your price range and have at'er.
Greg
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