Probably the most popular way to go is with a tube amp that offers good clean tones. This works for a jazz player who also plays blues or rock or country or whatever. The basic Fender (Twin, Deluxe, Blues Jr.) and Vox (AC-30 or 15) amps work fine for jazz.

However there are a couple of options that don't get used as much in other genres. There are a number of solid state amps that are popular in jazz: the Roland Jazz Chorus and the Polytone minibrute are two that jump to mind. Another type of solid state amp that gets used are "Hi Fi" amps like those of Acoustic Image. (I'd love one of those for bass and keys).

Thanks much for the info I appreciate it!

I have a Jazz chorus 77, its a smaller version of the 120. Its has a great clean tone. It has worked well on the jazz artist I have recorded.

In my experience with listening to jazz music and playing in jazz bands, jazz guitarists seem to like really bland, stale clean sounds. A lot of jazz guitarists seem to prefer solid state amps. And of course, there's that crappy bassy sound that a lot of jazz guitarists seem to like, so 15" speakers will help out in that department (at least that's what a lot of jazz guitarists seem to be using). Maybe jazz guitarists want an ultra-consistent sound? I prefer the randomness of a cranked tube amp, but to each his or her own.

Yeah, because having a big, deep and sexy 15" long excursion sub pumping the bass out is soooo crappy.
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randomness of a tube amp? What amps have you been using? Most designers take great pains to ensure their amps have a consistent tone.

Maybe what they really meant was " dynamic expression" rather than "inconsistent". Many tube amps for guitarists are designed to be pretty dynamic in pick response, sometimes this comes across as "inconsistent", because of the tonal changes that take place due to picking dynamics.
I, too have a nice little Jazz Chorus 77 combo and it is a fave amongst the jazzers. Several of the local players also seem to like the Fender Princeton Chorus, a solid-state amp with the personality of a dead fish, IMHO. Go figure...

My guess is that the best word for what he is talking about is "nonlinearity." Tube compressions and soft clipping are nonlinear effects that change to tonal response to louder signals. With a solid state amp you get (essentially) the same tone at all volume levels - linear amplification. Same thing is true for a tube amp driven well below the range where it distorts.

Thanks guys now it make sense. Like the Tube rectifier concept...thanks