Let me start this post by saying I think the 2013 version of the Sox can certainly contend. A few things break right with the pitching staff and I think the Sox will be right in the thick of the playoff hunt. That being said, the odds of the team taking home a championship this year are slim, so I'm gonna jump ahead two years and take a look at what I think the team will look like in 2015, when hopefully the team will be in better shape. I'm going to avoid the bullpen, because bullpens are too volatile year-to-year for any sort of prediction.
Catcher
Ryan Lavarnway is obviously the catcher of the future for the team and hopefully by 2015 he'll have established himself as an above-average Major League backstop. Lavarnway's minor league numbers suggest he has a ceiling of being one of the top offensive catchers in the game, but he's yet to live up to the potential. Should anything go wrong, the team could look to re-sign Saltalamacchia this offseason, but he could command more money on the free agent market than the Sox are willing to spend.
First Base
First base may be the hardest of all positions to project. It's certainly possible Mike Napoli could still be in town, but I would think he would get the bulk of his playing time taking over the DH spot for Big Papi. I don't think the everyday first basemen for the 2015 Sox is on the team or in the system. I believe the team will try to acquire a big name bat to fill the hole, similar to the Adrian Gonzalez pickup of a few years ago, but hopefully with better long-term results.
Second Base
You gotta believe it's gonna be old Dusty Two-Sacks holding down the second base position in 2015. The team holds an $11 million dollar option, that would presumably get exercised, unless something goes terribly wrong. It seems like he's a lot older, but it'll only be the Muddy Chicken's age 31 season, so he should still be a few years from a significant decline in defense or offense. Hell the team, may even have him locked up to longer contract long before they ever have to exercise the option.
Shortstop
Top-prospect Xander Bogaerts is the odds on favorite to take over the shortstop role in the next few seasons. If things break right Bogaerts could be entering his second season with the big club and looking for a big sophomore year. It's possible he gets moved to third before 2015 though, in which case the team will probably still be plugging in stopgap players as they seemingly have been since Nomar left town or hoping prospect Deven Marrero is a keeper.
Third Base
Hopefully by '15 Will Middlebrooks will have established himself as solid above-average third basemen. His rookie campaign would certainly suggest he's heading in that direction, but questions about his on-base ability may hamper his stock before 2015. As mentioned earlier Xander Bogaerts also may have moved over to third by this point in his career, in which case the Sox may have to move on from Middlebrooks, whether he establishes himself as an outstanding trade chip or if he fades into a backup role.
Outfield
Jackie Bradley Jr., Jackie Bradley Jr., and Jackie Bradley, Jr. C'mon, he's awesome, he can play three positions at once right? OK, maybe not, but hopefully by 2015 Bradley will have a year of patrolling center under his belt. Left and right could still be question marks though. Shane Victorino will still be under contract and could very well still be an effective player. If not he should be a solid, if overpaid, fourth outfielder. Another top prospect like Bryce Brentz could also be ready to take over an everyday role by then, provided he's not shooting himself in the leg on a regular basis. Outfield could also be another spot that the team looks to acquire a big bat either through free agency or a trade.
Designated Hitter
As I alluded to earlier, if Mike Napoli is still kicking around (which would presumably mean his health issues haven't caused too many problems) he'll probably see the bulk of his playing time at DH. If Napoli's long gone by 2015 though, it's anyone's guess what the team will do. Most teams nowadays like to use the DH to give position players a break from the field, so it's certainly possible that's the direction the Sox go.
Starting Pitching
Starting pitching could go a lot of ways for the Sox. On one hand they could still be looking at a staff anchored by Jon Lester, Clay Buchholz, and Felix Doubront. On the other hand the Sox could be looking at a staff filled with youngsters like top prospects Matt Barnes, Allen Webster, and Rubby De La Rosa. Buchholz will be set to make $12 million in 2015, so he seems like a safe bet to be kicking around the team still. Doubront will be in his first year of arbitration, so if he's continues to progress, he should have at least a bullpen slot. Lester however is only signed through 2014, so the future's anyone's guess with him. If he returns to his pre-2012 form, the team will hopefully have locked him up to a longer term deal, but there's no way of telling at this point. Which free agents or prospects will fill out the rotation is anyone's guess, but if I had to guess it'd be at least one of the three aforementioned prospects and a moderate-to-high priced free agent/trade acquisition.