okay here we go:
XLR: Microphone cables, or high grade balanced cables. Balanced means, that even if the cable is longer than 6 metres, there will be no humm and no significant signal loss.
picture of an XLR cable
RCA: The red or black or white plugs, mainly used for HiFi equipment (cd players, home audio etc)
picture of an RCA cable
Jack: This is the stuff musicians use most. They are straight-forward silver plugs, and connectors are featured on about anything: guitars, mixers, keyboards, speakers (active) and many more.
Picture of a Jack cable
Digital: This is more of a studio grade product, which, for home recording, would not be neccesary, unless you're experiencing humm or buzz
I've not heard of "aes ebu"....sorry, can't help you on that.
MIDI is not a sound cable, it is used to transmit commands, like: "switch to that amp type with that effect at volume 55 and...." etc. It's also used with keyboards: "hit a high C at volume 80 with sound program 67 and sustain turned off"
It will not transmit the real audio signal, so for recording your guitar (that's what you want to do, right?), you should use either the jack or the digital cables, if you have a digital input on your pc.
You should plug the V-amp into the LINE INPUT, not into the MIC INPUT -- very important.
I don;t know how experienced you are computer-wise, but here's the deal:
just make sure your audio card's mixer levels are good, so turn up the LINE IN fader, and leave the other ones.
I don't know how Adobe Audition works, so someone else has got to help you on that.
Good luck with it!