It’s a good question. I think that priority free agent additions are at positions where you need experience and fairly immediate contributions. Overall, they should fill EVERY major need in free agency, but I’d put Defensive End and Center/Guard as the main focuses right off the bat.
You also will likely see additions at receiver, defensive back and running back as well. Maybe not guys who are expected or needed to start, but more of mid-to-low range free agents. Guys who were stuck on bad teams, had bad luck with injuries or just want one last shot.
Sometimes those guys work out (Mark Anderson, Alge Crumpler, Andre Carter) and sometimes they don’t (Marcus Benard, John Lynch, Torry Holt).
The goal is to go into the draft with no needs, especially not at the top of the depth chart. Eventually every position could be a need in-season, so you just have to take players who fit in New England and can play for BB.
As a result, sometimes depth is a little thin at positions. They got by with basically two defensive ends this year, but their lack of depth at defensive tackle came back to haunt them somewhat.