Realistically . . .
OFFENSE:
QB - I think we'll see a older veteran "camp arm" guy - someone who'd pretty close to having played out his string even as a backup (pretty much everybody on the list). OTOH, if the Pats sign one of the better guys (maybe Josh McCown or Shaun Hill), one who could conceivably hang with the team, it might indicate that something is afoot wrt Mallett's status and a potential draftee.
RB - Personally, I think it would be a disaster if the Pats can't re-sign Blount. I don't think his demands will be unaffordable, but . . . In that unfortunate event, Ben Tate or even MJD might be worth a conversation. One of the lesser guys (Starks, Bell) might be brought in to compete with Bolden, anyway.
WR - Re-signing Edelman is a must, but there's probably a greater chance that he gets an unmatchable offer elsewhere than there is with Blount. If he can't be re-signed, that changes things radically. It might bring Emmanuel Sanders back into the picture. Whether Edelman re-signs or not, I think Collie gets another 1-year shot. And, I'd kinda like to get Tiquan back, myself. Like this past Camp, I think we'll see a couple lesser vets, maybe Kevin Walter, Jerome Simpson, possibly Meachem. The exact "who" depends on what kind of influence BB thinks a guy will have on the team's young WRs and how he projects the future development of Dobson, KT, etc. (We might even see yet another WR draft pick, and almost certainly another couple UDFA WRs.)
TE - This is where things get interesting. First, I'm pretty sure that Hooman is re-signed. He's a solid backstop and ST player who knows the systems and will be cheap. Next, I think we might see a guy who's been a decent blocker and likely to be more productive as a receiver than Mulligan - maybe Dickson or Quarless. I'm guessing that the Pats will be easily outbid for guys like Chandler and Pettigrew by teams who are willing to overpay. If BB's plan is to draft another TE (or two), we could see an older vet like Dallas Clark (if he decides not to retire) or Fred Davis. Somewhere along the line, though, it seems like there has to be a new "move" TE who's mostly a receiver. If the coaches don't think Harrison could cover part of that role, the guys would probably come from the draft on Day-2.
OT - A couple 2013 UDFAs still hanging around for potential development in their 2nd year and draft weekend might bring another. Svitek probably get re-upped for another year.
OG/OC - pretty much the same as OT. Wendell probably gets a new contract, whether the majority here likes that or not, with guys like Kline, Barker, etc. in development behind him (and Connolly). In any case, it's unlikely any of the FAs with any starter potential will be available at reasonable money.
DEFENSE:
DE - The FA's who'd be likely to have an immediate impact are all likely to be too expensive - including Arthur Jones, unfortunately. One of the older guys, maybe trying to find another Carter, or one of the younger guys who hasn't done well elsewhere, and/or a late-round flyer in the draft are the affordable avenues. The Saints seem almost certain to cut Will Smith who BB has long admired. His 2014 cap number is $13.9M, but his dead money hit is only $2.35M.
DT - Maybe another older (cheap) vet for camp and probably a draft pick at some point, but Siliga seems like he may be enough to lessen the need to spend early.
LB - Seems likely to me that BB could grab a 2nd-tier FA as depth going into the draft where I think he may take a flyer on one.
CB - I'm thinking that BB signs a FA, the quality of whom may be in inverse proportion to the likelihood of Talib being re-signed. There's actually a lot to choose from this season.
SAF - Adrian Wilson my be in the "didn't pan out" file. Tavon Wilson - it's hard to know. Just because he's at the bottom of this depth chart doesn't necessarily mean he's awful, but ... There are a few vets on the FA list who could be okay depth signings (like Adrian Wilson), and a late-round/UDFA signing is probably in the cards anyway.
Bottom line, as always, is that we can make all the wish lists we want, but we're unlikely to see a big name FA signing for the 2014 roster.