I firmly believe letting Buxton go would be a slap in the face. If he wants to leave, that's one thing, but if he's willing to stay then keep him. Not apples to apples, but in my mind it would be like when they let Rod Carew go to the Angels. Buxton is Twins Baseball to so many fans, whether serious or casual.
Ryan while good, I don't the loss would break the team. Since Lopez should be back next year, and with quite a few promising younger faces in the starting lineup (Bradley, Abel, Prielipp), Ryan has enough value to make it worth considering. I'd hope we would keep Ober - considering what he could do to the Marlins even with a diminished velocity, I think he can still pack a punch.
To me, Jeffers is the obvious goodbye. Is he an amazing catcher? Yes. Does he add some serious value to the team both offensively and defensively? Duh. As much as it hurts to say, that's the problem. He's probably too good for where the Twins are right now. He has the skills to be on a World Series team, and that's not something that I think will happen for us.
Bell is one that I think should be seriously considered. If we can get something good for him, let him go. As fun as our "For Whom The Bell Tolls" rallying cry is, we could trade him out for pretty much any streaky first basemen with similar results. And I think a younger model would come with some pluses.
Martin is one we need to try and keep. While he's been struggling recently (minus last night's GLORIOUS home run!), when he's hot he's HOT. I'd rather keep the almost guaranteed single/double in the lineup.
I don't know how much value Lee has for trade, and I think it's too early in the season for me to say anything concretely. He's pretty solid infielding, but yes, the batting is streaky at best. I don't know how much value he has, but if no one is willing to snap him up, I don't think keeping him is going to kill our chance of competing.
Larnach seems like another obvious one for me, especially since he's doing better. As another comment mentioned, we have young guys that we could bring up to take his spot, and I think we should jump on that.
The Twins have always been a farm club, let's see what that crop can yield!