Stats are the big thing in baseball nowadays. Maybe you're thinking, "Sure, I follow stats all the time" and maybe you do, but if you are not among the sabermetrically inclined you may be behind the times a little. These aren't the stats that are on the back of your old baseball cards. These stats try to go a lot deeper and explain the true value of a player by isolating the kinds of numbers he has the most control over. This isn't intended to be an exhaustive look as much as a brief intro. This post isn't intended for the advanced stat guy.
Stats to look for in hitters:
Walk rate - This is important in two ways 1) People who walk more tend to get on base more, therefore they create run scoring opportunities for teammates and 2) hitters with higher walk rates tend to be more disciplined at the plate and swing at better pitches. If a minor league player is a successful hitter in the minors with a low walk rate, he may not be able to carry that success into the majors because experienced pitchers will exploit that hitter's aggressiveness and make him swing at pitcher's pitches. Now, some hitters like Vladimir Guerrero or the younger Alfonso Soriano could hit those pitcher's pitches anyway, but they are the exception to the rule. If you read my blog on Starlin Castro, you may also remember my statement that not all walk rates are created equally. Castro does take a lot of pitches, but he also makes contact more often than most players so even if he takes a few pitches, he's more likely to put the ball in play once he does swing. This may limit his opportunities to see enough pitches to draw a walk. Others, like Alfonso Soriano, simply swing at just about everything that gets up there. Though walk rates don't normally take significant leaps, someone like Castro is more likely to improve on his walk rate than Soriano did over time. An average walk rate is 8.5%. Castro's most recent walk rate is 8.2% at AA and provides some hope for the future, though that was in a limited number of plate appearances.
OBP and Slugging Pct. - If you have a low walk rate, you better be a .300 hitter to get your OBP up and/or hit for some power since doubles, triples, and homeruns are obviously more valuable than singles. Sometimes you'll see the two added together as OPSv(On-Base Plus Slugging). I'm not a huge fan because the two statistics are weighted differently but it's a good place to start if you're trying to determine a player's overall offensive value. Some sabermaticians have come up with better statistics such as wOBA (weighted on base average) but that's a stat for a different day. The bottom line is that hitters, to some degree, can control how often they get on base and how hard they slug the ball. What they can't control is how often their teammates are on base to create RBI opportunities. So a sabermetrically inclined fan may tell you, therefore, that RBIs are pretty worthless when determining a player's individual value.
BABIP - This stands for Batting Average on Balls In Play. This is a statistic that tries to eliminate luck by determining what your average is when you actually make contact. Putting it simply: If you are getting a lot of bloop hits then your BABIP may be unusually high and conversely, if you're hitting a lot of line drives right at someone, you're BABIP will go down. The thing about BABIP is that you cannot sustain good or bad luck for a long period of time, eventually it finds it's equilibrium; what statisticians call "regression to the mean". The league average for BABIP is .290, though this can vary depending on the hitter. If you're Ichiro Suzuki, for example, you get to first base extremely quickly so you'll have a higher BABIP simply because you will beat out groundballs for infield hits that others wouldn't. A power hitter such as Albert Pujols may also have a higher BABIP because he hits the ball harder. He hits more line drives which are much more likely to get past fielders than if you are Aaron Miles and hitting pop-ups. The good news for Cub fans is that both Alfonso Soriano and Geovanny Soto had unusually low BABIPs last year. This likely means that they will bounce back a little this year. But if you've been paying attention, you might say, "Couldn't part of Soriano's drop in BABIP be due to his loss in speed?". That would be a valid point. If the injuries have permanently affected his speed, then his BABIP may not ever be as high as it was in his youth. However, it still should bounce back closer to his career BABIP average of .306 instead of the .279 BABIP he had in 2009. Since Soriano hit .241 last year, you should expect him, all things being equal, to get his average back in the .260-.270 range. BABIP is just one reason that stat-minded people don't value average as much because some of it is dependent on luck and how many of your batted balls elude fielders. Unfortunately, luck has nothing to do with Soriano's inability to catch the occasional fly ball. That's all him.
So this is a brief intro and a little oversimplified but it should give you the basic idea of the kinds of numbers people are looking at nowadays. I prefer to combine numbers with scouting reports and personal experience, because while the numbers can tell you a lot, they cannot tell you everything.