Probably your best bet is use Google to research the different types of guitar synths available. Personally, I'd probably stick with Roland since they've been the forerunners in guitar synth technology for a couple of decades now.
I've got a really old GR700 and use it for about 90% of the midi stuff I do. I rarely use the built in sounds cause it's very 'analogue' sounding compared to newer synths, but for techno leads etc, it's perfect.
I've got the 808 guitar to go with it so it's got all the controls for blending the guitar/synth sound and various other things like sensitivity.
Having the custom guitar for the synth also allows you to use a 'touch' plate to activate the vibrato. (a little brass piece attached to the pickup that completes an electrical circuit when you touch it at the same time as you touch the strings.)

For live work you might want to look into getting a keyboard volume pedal customized so you can rock between the synth and guitar sound.
That way you can play guitar and gradually fade in the synth sound by using the pedal.
Another use for the guitar synth is to trigger loops or samples. ie, hit a high e and it plays a sample of 'eruption' through your synth.
You can also use it to trigger functions in your recording software.
For instance, play a low E and certain other notes and it will start/stop/rewind/record your software etc. So you can stand in the middle of the room, and by playing certain combinations of notes, you can change the patch, activate your recording software, play a sample, stop the software, rewind to the beginning, play the recording back, all without touching the computer.