I have had a lot of fun roleplaying with a monster character that has very low INT. It is good for some laughs and it is challenging for me to turn off that common sense/thought processing part of my brain and have my character act accordingly. (He does have a high Str/Con and a natural regenerating ability that helps keep him alive in the most dire of circumstances.)
To answer the original question, Constitution has to be the one. No matter what character is generated, more hit points never hurts.