With the exception of catcher, the Sox aren't necessarily going to see any changes in their starting lineup; of course, they could sign Texeira and jumble everything up. Left to right in the OF is Bay, Ellsbury, and Drew. 4th OF is up for grabs, with Coco having been traded away and Kotsay a free agent. Especially with DL Drew on the roster, a capable 4th OF is a high priority. Defensively I'd say this is an average OF. Bay is a bit below average, Ellsbury has great range but no arm, and Drew gets a good jump on the ball but doesn't have blazing speed, and his arm is perhaps a bit above average.
In the IF, Lowell & Lowrie will work the left side, while the Sox boast the best right side IF in all of baseball, Youkilis & Pedroia. Lurking/sucking in the wings is Julio Lugo, who is still under contract with the Sox. Lowrie is probably average at best defensively at SS, as his range is pretty limited but he has sure hands on the balls he gets to and while not possessing a cannon, throws accurately and turns the double play pretty well. Lowell, Pedroia, and Youkilis are all excellent in the field, so defensively the Sox IF is pretty darn good. There's also a decent amount of flexibility by position, as Youk can play third while Lowrie has seen action at both second and third should the situation arise. The role of backup middle infielder in the past has gone to Alex Cora, but if the Sox aren't able to unload Lugo, they might be content to let him rot on the bench in that role this year. I suppose I'm fine with that.
As for hitting, Pedroia, Youkilis, Drew, Bay, & Lowell (if fully healthy, which he appears to be) are pretty much known quantities at this point, so as much as one can predict the future, they're likely to post similar numbers as last year. Ortiz, as mentioned yesterday, has more uncertainty, but what isn't uncertain is that he'll hit third and the Sox fortunes on offense will rise and fall with him.
Ellsbury was pretty uneven last year, starting off hot but then tailing off for pretty much the whole season, and not doing much of anything in the postseason (indeed, Crisp started several games in the ALCS). Since it was his rookie year, one would hope that he'll be better this time around, especially in terms of drawing walks and getting on base, where his speed is lethal. The Sox other starting rookie, Lowrie, ended the year with a 0.739 OPS, which, if he had enough at-bats, would have put him in the top 50 in the AL. So with some improvement, Lowrie could be a decent contributor. Indeed, how much or little these two now-second-year players improve will go a long way in determining the success of the Sox lineup.
Various statistical analyses have been done to show that, over the course of a 162 game season, lineup construction really doesn't matter all that much in terms of how many runs you'll actually score, but it is still fun to think about. The heart of the Sox lineup, from 2 - 6, is pretty darn good, with Pedroia, Ortiz, Youkilis, Drew, & Bay, which nicely alternates R/L. Lowell makes for a good 7th hitter. If, and this is a big if, Ellsbury can improve the point where he's a solid lead-off hitter, then this is a truly good lineup. Heck, it wouldn't surprise me if Lowrie actually showed more improvement and he ended up leading off. The only weak spot is catcher, whether it be the corpse of Varitek or some scrub they bring in.
Last year the Sox scored 845 runs, good for second in the AL behind only Texas. Of course, that team had Manny for half the season, although Bay did a reasonably good Manny impression when he arrived in August, putting up an OPS of 0.897 with the Sox (Manny's '08 Sox-only OPS was 0.927). Given that not a heck of a lot has changed since last year (at least not yet) I think the Sox will perform about the same on offense, with some room for improvement, if either Ellsbury makes some headway or Papi stays healthy. It is not a lineup that will wow you with homers, but they work the count, get on base, and above all, actually score a lot of runs.