All but certain to have spots: Capps, Nathan, Mijares, Jim Hooey
Capps is likely the closer with Nathan's role depending on his recovery. My guess is that Nathan will pitch in a back of the bullpen role to start while they test his arm. Hooey apparently is a hard thrower with a fastball in the mid-upper 90's. If he gets the ball over the plate consistently he probably fits a setup role. Otherwise he is one of the middle relievers. Mijares is the left-handed setup guy and may be called on as the main guy to get the ball to Capps.
That leaves three openings. I think the front runners for two of those positions are Perkins and Neshek. There have been mixed reports on Neshek, but he apparently lost velocity as the season went along in his first year back from surgery. If he shows up throwing hard in spring training he is likely to start the year in either a setup role or in middle relief. Perkins appeared to have fallen out of favor, with lots of predictions that his days with the Twins were over. But he appears to have rejuvenated his reputation with coaches with his performance last fall. If that performance carries over to this year, he will likely be in a middle relief role.
The competition for those two positions and the seventh spot in the bullpen can be split between two groups. One is a group includes Burnett, Slama, Delaney, Manship and Diamond (their rule 5 pick). Burnett started out well in the bullpen last year and then faded as the league caught up to him. But he is still young and has major league talent. He would likely be the favorite for the 7th spot. Manship, Slama and Delaney are all pitchers who could take the 7th spot by default. They are old enough that sending them back to AAA for seasoning is probably not an issue. They need to show they can perform in the major leagues, but their chances to do that probably depend on more talented pitchers not being ready. Diamond is a wild card. Some speculation is that he could be a situational lefty. I think whether he makes the role depends not only on his own performance, but how confident the Twins are in the six guys they have ahead of him in the bullpen. He probably is not going to be the best pitcher of the group, but the requirement that he stay in the big leagues may win out if the Twins think they can carry him in the back of the bullpen.
The second group is a bunch of young prospects. This includes Guttierez, Swarzak, Waldrop, Robertson, Province. These guys are probably all slated for AAA. With the possible exception of Swarzak, they will have to step up in spring training and force themselves onto the roster. Guttierez is clearly the guy with the most upside. If he does well at AAA, its likely he will be in the bullpen by the playoffs. Swarzak has had opportunities as a starter in the past, but he has probably been passed by on that list. He still has some time to develop but the clock is close to run out. Waldrop, Robertson and Province are all guys with some talent, but little experience above AA.
Finally, there is one other possibility. If the Twins sign Pavano, then one of the current projected starters (Slowey, Blackburn, Duensing, Liriano or Baker) will likely end up in the bullpen. With the exception of Duensing, I think they are all out of options, so having them start at AAA is not an option.
To summarize, there are lots of questions with the bullpen, lots of answers and a lot of sorting out to do. I think some of it will get sorted out in spring training, but it is not unlikely that, like last year, the bullpen is a work in progress for most of the season. The best case scenario is probably that Nathan regains his form and pushes Capps into a setup role along with Mijares. Hooey shows command of an overpowering fastball. Perkins and Neshek demonstrate the potential they were believed to have and Guttierez comes up and provides an additional dominant arm for the playoffs. More likely several players fall short of those lofty goals or get hurt. Then the Twins will be looking to deal for additional relievers at the deadline.