Interesting thread..... even though it is from a carrot cruncher
As someone who went the other way, from guitar to sax, I think it should be pretty easy for you. As always, listening to your favourites is the best way.
I have played jazz guitar pretty seriously for 20 odd years, and owned probably 30 guitars over that time, GAS is a full time problem for 6 stringers.
If you tell me what sound you are after, even a specific track/recording, I should be able to advice on guitar/amp combinations
For jazzy stuff, you can use pretty much anything, but for an allround electric guitar you cannot beat a telecaster, it goes from jazzy in the neck pickup position to country twang. It also benefits from stable tuning, and good residuals for resale
Acoustics can be limiting, and difficult to amplify/record. They can also be tougher on the fingers for a beginner, due to action, nut spacing and string guage/tension. I learnt as a 12 year old on nylon string, which I still use for Bossa Nova style playing. These are easier on the fingers, and a good starting point. I have a maccaferri style guitar for out and out gypsy stuff, but these can sound terrible if not played with some verve (and skill)
If you want an acoustic, try one first, and make sure it "sings". Some of them can be lifeless and frankly disappointing.
I worked in a guitar shop in my 20's, and saw lots of beginners come and go. My suggestion would be a Fender/Squire Tele, and a small (fender?) practice amp, with reverb, which flatters the beginner. You won't be dissapointed. If you love, and only want, the mellow jazz sound, you could go for a cheap semi, a Gibson 335 or 175 clone. These have a limited tonal range though, and I could do a blindfold test with my telecaster thinline and my Gibson 175, and most couldn't tell the difference. I have played out using my tele on jazz gigs, and although it raises eyebrows, it sounds fantastic. I can make a tele sound like Wes, George Benson, Barney Kessel, Jim Hall etc so ideal for jazz comping. It can be bright, but rolling off the treble is easy. I once had a nice chat with Jim Mullen after a gig, and he told me that he only uses a "Jazz" full size semi because it looks more appropriate, and he was sponsered by Aria. He likes the telecaster for jazz too.
BTW, I find playing the piano helps my sax playing more, as the chord notes are kind of "layed out" in front of you. The problem with the guitar is that you tend to work in "shapes" rather than notes. You will learn finger patterns for chords and scales, and this won't neccesarily help you sax playing. BUT the guitar is good fun, so go for it!
I would be more than happy to post some soundclips for you of various guitars so you can get a feel, just let me know.
If you click on my soundclick link below and listen to "cry me a river" this was recorded using a USA 90's telecaster thinline straight into my multitrack.....
The terrible solo (03:25 onwards) in my latest offering "the shadow of your smile" was recorded using a full bodied Guild X-150 Jazz Guitar into a mic'ed Fender Vibroverb valve amp from 1973. This is probably the archetypal jazz set-up, and you can certainly sound like Wes on this. You mentioned slide though, this would sound muddy and horrible on this set-up. Better on the telecaster....