Sanzo himself: Sanzo was found as a baby on the banks of a river by his predecessor, who helped to bring him up, until the day that Koumyou Sanzou was killed before him by demons just as he named little Sanzo as his heir... Well that's where Sanzo got his hatred of demons, so he's not best pleased to find that he has to go on a mission to the west with three demons...
Sanzo likes to keep himself to himself and always has, so the antics of the others sometimes has him pulling out his deadly paper fan and stomping on heads. That's when he's not punching the bad guys in the chops and blowing there heads off... and when he's not being inconvenienced by the world at large, he's got his reading specks on going through the paper while chain smoking.
Despite all his cold heartedness, the other three do seem to get through his cold exterior. I mean would you drink yourself into a stupor with people you didn't trust? as they all do when ever they can. he also smokes like a trooper... All in all he's not your normal holy man and hates everything, thought saying that he dose have his reasons for being a surly bastard.
His uses a gun to kill anyone who piss's him off, even though he is a Buddhist priest, he had no qualms about killing if it might mean his own life.

His Relationship with the Others:

Goku = He cant get rid of the brat, he only rescued Goku because he was fed up of the demon calling him subconsciously and since then has been stuck with him.
On the outside, Sanzo treats him as he does everyone, but on the inside Sanso couldn't live without the little brat, and shows amazing bouts of affection for Goku on odd occasions, mostly I think he sees Goku as himself as a child, when Koumyou Sanzo used to look after him.

With Hakkai = He talks to Hakkai reasonably, mostly because the demon doesn't get on his nerves so much and keeps the other two in line. If anything I would think he respects Hakkai the most.

With Gojyo = You would think that he would be a little more closer to Gojyo with him being at lest half human, but they don't really seem to have much in common with each other, other than to bum fags off each other.. (oops "Borrow Cigarettes of each other", the American translation :P)