I'll focus on the "Big 3" first, Welker, Vollmer, Talib.
In my opinion, whether Welker stays or goes will depend completely on whether a 2 or 3 year deal can be had. If not, then Franchising him would cost over $11m and effectively eat away the team's ability to pursue other quality FA without having to make roster cuts or pay cuts. Welker is important to this offense because the offense is designed around Welker. If he can't be had at a reasonable cost, (no more than 8m per year, imo), then he needs to be let go. There are more than enough weapons on this offense to get by, Josh just has to retool its concepts.
Vollmer should be the team's priority. When healthy, he is an absolute monster that can play both RT and LT. That's amazing... when healthy. His back issues are a red flag, as is his probably desire to be paid like a LT, since he has shown he can play that position and LT are always in demand. The Patriots may best be suited to Franchising Vollmer and trying to work out an extension with him over the next year within the evolving economic makeup of the team. If that fails, hey, at least the team managed 1 last year out of him.
Talib is intriguing. Bill admires what he brought to the team, and Talib has expressed some admiration with the Patriots. There is no denying he made this team better. Whether Bill or Talib feel he stays is another issue, and will likely come down to dollars. Despite health concerns and character issues, today's NFL pays any average CB like they're top tier (Jason McCourty, Finnegan, Carr, just to name a few recent examples). Talib's mindset will likely be to cash in while he still can. If that's the case, there is no way the Pats can afford to retain his services. The only way Talib sticks around is if he hits the FA market and finds teams are turned off to him, or if he and Bill have a sit down, discuss the past, and settle on a 2-3 year deal at maybe a little over $20m. Even that's a lot. If it exceeds that offer, he's gone.
Woodhead is a coin flip. He and Vereen are the same player in terms of skillset, and it will be up to the coaches to decide whether Woodhead's value has been replaced with Vereen, or whether they desire to retain him for additional depth. There is no questioning that Woodhead's value is greater to the Patriots than it will be elsewhere, which makes me lean toward him staying.
Edelman should stay because he should come cheap. He has dealt with injuries throughout his career which have ultimately stunted his growth. Until he shows he can stay healthy, he won't be shown any big dollar contracts. Edelman is a versatile weapon. He will never be a focal point of any offense, but he complimentary skills and ST abilities should help him stick.
Arrington is gone unless better can't be found. His ST value is marginal, and he is only AVERAGE when in the slot. Then again, Bill seems to like him, so he may be back. But I think better can be had.
Thomas will likely go because he has shown starting capability during his time here. He performed decently, but there are enough teams out there that will look at him as an upgrade.