I've been updating all my gear this year, new strat, new amp, now I'm looking to satisfy my jazz needs with a nice semi-hollow electric guitar. My price range is no more than £600, which is pushing it. I won't bother converting that into $ because UK prices are grossly inflated compared to America - just let me know about any mid-range guitars if you're from that part of the world.

Epiphone Casino
Epiphone Sheraton
Epiphone Dot
Epiphone Joe Pass
Epiphone ES-175

Hofner J5

Washburn J5

Adam Black JA 20

Hagstrom Viking

Pretty much all of the Ibanez Artcore series.

Hope this helps.
id go for an artcore, i tested i against an epiphone dot and mine beat it easily, very nicely built and great sound
Gibson SG Standard

Custom Monterey Strat with Half scallop and CS 69's

Marshall Class 5

EHX Big Muff
- Any of the Epiphone's. There's a reason why their top archtops cost more than even the top Gibson archtops. There's a video somewhere on YouTube of a stock Epi Dot being played against a twenty year old Gibson 335, and the difference is almost unnoticeable, which considering the price difference, is incredible. For £600 you could get a good Epi archtop, and with a couple of mods (I would definitely suggest changing the pickups, which are the main area that the Epi's fail at), you'd be set. Hell, I've got an Epi Dot Studio (the very cheapest and most basic archtop they do, it's under £200), that with just a pickup change (Gibson BurstBucker #2 reverse polarity in the neck and #3 in the bridge - totals about £280 or so), I've been able to comfortably use for gigs, and everyone's been impressed with the sound, before even knowing how little it cost. I really can't stress enough just how good the Epis are.

- After that, Ibanez Artcores. Better stock pickups (though I'd still advise changing them), slimmer necks, slightly better quality bride/tuners/mounting rings/etc. My issue with the Artcores though is they never sound quite as 'classic' as any Gibson or Epiphone archtop will, and I've generally never been that impressed with the Ibanez build quality (for solidbodies, I find ESP/LTD produces much better quality instruments at the same price - for archtops, Epi do better). Still, the slightly more modern voicing and slimmer neck might suit you perfectly.

Try both out and just see what suits you more. The Epi's are more 'classic' but will need some adjustments before you could gig it, the Ibanez come with slightly better features straight off the shelf but is slightly more modern.