My first question is, what format is "better," CD's or vinyl records? And by better, I mean which is more accurate to the original source?
CD, by a mile. You can make a digital copy of a vinyl record that is audibly indistinguishable from the vinyl. You cannot make a vinyl copy of a CD (assumng you had a record plant!) that sounds just like the original CD. Digital is transparent; analog is not.
but I keep hearing from many that they sound better then CD's
Indeed you do. Part of this must be nostalgia (or retro appeal, depending on your age bracket). But it's also that vinyl adds a certain amount of distortion of a sort that actually quite appealing. Some people mistake this for "realism" (probably the nostalgia at work there), but of course it's that distortion that makes vinyl non-transparent.
Bottom line, CD is more accurate, but people like vinyl, and there's nothing wrong with that. I listen to both.
I stumbled upon the VPI traveler turntable which got a great review on Stereophile as well as other sites.
You would do better to pick a turntable at random than to listen to Stereophile. Their analog reviewer is the biggest boob in the business.
I'm with Class A on Rega vs. VPI. And you certainly don't have to spend that kind of money to get a decent turntable. Rega tables start around $400 or so. Pro-Ject and Music Hall also make sub-$1k tables; most come with decent starter cartridges.
Lastly, I have an Integra DHC-80.3 processor. I know the turntables are analog (obviously again) and that the analog signal would be going into the processor. Should I turn all sound processing off for this (like Audyssey etc)? With Audyssey engaged, it is my understanding that the signal gets converted into a digital signal for Audyssey to do it's thing to the signal, then converted back to analog which seems like it defeats the purpose. Is this right?
Depends on what the "purpose" is. As I said above, the digitization doesn't affect the sound, and if you use Audyssey for room correction when listening to CDs, why wouldn't you want to use it when listening to vinyl? It's not like your room nodes suddenly disappear when you start up a turntable! On the other hand, if you want that true vinyl experience, then direct analog pass-through is the way to go.