You are looking for a shred guitar to play warm and smooth jazz sounds like Pass' or Montgomery's when chorusing... that's not an easy job finding a true jazz-guitar with 24 frets and a whammy bar... Try looking fusion/funk oriented guitars.
If you don't care about the characteristics of the guitar, get gibson or ibanez hollow-body jazz guitars which have been named by every answerer there.
My best advice is my current rig, which provides me a thick and convincing jazz-sound, being a fusion-rock setup though :
A Parker Fly with Seymour & Duncan pickups. That Mahogany body with the S&D Jazz pickup is simply incredible. Associated with the piezzo bridge bickup you can get a lot of different very convincing jazz tones.
You can also try guitars like Vigier or, even better, PRS (I know there is a little semi-body PRS that must be incredible at jazz music, and that still have 24 frets and a whammy bar), that have almost the same characteristics.
By the way, you will often see guitarists using Parker guitars gigging in a funk-fusion-jazz style, they are probably the best solid-body guitars when it comes to imitating a classic jazz sound.
Any good and versatile tube-amp on clear tones should be worth it... The Peavey Classic Series or Vox AC Series (Peavey Classic 30 and Classic 50, Vox AC-30) can be a quite good choice as they are not so expensive and quite good at clean and soft-reverb sounds, but Fender Accoustisonics or Twin amps or, even better, the Roland Jazz Chorus are ultimate if you can find and afford them. Forget Marshall or Mesa Boogie Amps for awesome clean warm tones.
If you are looking for simulations, I know the Vox Tonelab multi-effects to be very good at clean tones... If you are looking for effects, some chorus, delay, reverb... eventually a tremolo can be nice. And also equalizers.
My little advice : try to plug a good equalizer pedal directly after the output of your guitar, before any other effect and amplification. If you lower high frequencies (but not harmonics), and strenghten low-medium frenquencies, and if you play with the tone button of your guitar, you should get a warm tone with any guitar you play.
The Dunlop MXR 108 pedal is really worth it and not really expensive... and you will use it for all types of musics when plugged like that. I really use it everywhere, it is probably the only element of my rig from which I couldn't separate or exchange.