Stats
OPS is the best freely available stat to look at when it comes to offensive production, it correlates to run production much more than a stat like Batting Avg. In fact, you can basically disregard all the other traditional offensive stats.
When looking at pitchers I like to see how they have done against the opposing lineup according to OPS. An OPS of .800 or greater is solid for the offensive players, but you want to see a high number of at-bats. A player who has a .950 OPS in 7 at-bats against a pitcher is less impressive than a hitter with a .875 OPS in 70 at-bats. You can trust the .875 hitter's production to a higher degree.
In addition to OPS against, when evaluating pitchers you want to look at stats like DIPS ERA, a stat found on the ESPN site for one. These stats will alert you to pitchers who are pitching better or worse than their ERA would indicate. Pay special attention to park effects, a pitcher in SD can have a misleadingly low ERA while a pitcher in ARI can have a misleadingly high one. Also, when looking at present form of a pitcher check his recent strikeout, walk, and home run rates and see if they are improving or not.
As far as bullpens go it can be time consuming to track the 4 or 5 pitchers who might get in a given game. Some sites provide some info on days rest, etc. If you have the time you want to incorporate this into your capping but if not just try and keep a general idea of whether the bullpen has been good or bad, without delving too deep into the specifics.
There are some good resources available like Baseball Forecaster and Baseball Prospectus that can provide more predictive stats, but their sites have a small yearly fee that some people might rather not pay. They are not gambling sites by the way, they are tailored to general baseball analysis and fantasy baseball, so you won't see any stats regarding a record vs. the spread.