It's almost impossible to predict the MLB draft, unlike the NBA and NFL, because it often takes years to break into the Bigs. Andrew Brackman was drafted in the first round in 2007 and is only in Low-A Charleston. The most recent draftees on the current team are Joba Chamberlain and David Robertson (both taken in 2006).
For comparison, the New York Giants first round pick last year was Kenny Phillips, who played in every game and was sixth in tackles. It's extremely rare nowadays to see a draftee play in MLB the year he's drafted.
Anyway, the consensus #1 overall pick will be (barring any unforeseen developments) Stephen Strasburg, a right-handed pitcher from San Diego State. There's not much hype surrounding him - he's only been called the 'best prospect ever.' His stats stand as such: 97.1 innings, 1.57 ERA, .79 WHIP, 133 K, 16 BB, 1 HR. He threw a 17-strikeout no-hitter on May 8th.
The Yankees could go any direction with the 29th pick. Baseball teams generally don't draft for need (again, because it takes so long to reach the majors, who knows what the 'needs' will be at that time), but the Yankees' MO in recent years has been to take high-ceiling RHP in the first round (Hughes, Cole, Brackman, Joba).
Sean Potter (of Pending Pinstripes) has the Yanks taking New Jersey high-school centerfielder Michael Trout. The Sporting News predicts Tony Sanchez, a catcher from Boston College. Project Prospect goes for Rex Brothers (sounds like a WWF tag-team, no?), a LHP from Lipscomb U (in Tennessee). MyMLBDraft.com sees the Yankees taking (finally) 6'6" RHP Kyle Heckathorn from Kennesaw State.