I expect the first FA we sign to be a very minor one (someone to provide depth/competition at a particular position), as I don't expect the Hawks to go 'all in' on any Michael Bennett/Desmond Bryant-type upper-tier FA's in the first couple of days (not that I'd mind if they did, though). So I'll go with Giants LB Keith Rivers, a former player of Carroll/Norton's at USC, to compete for the WLB job, and to provide depth at all 3 LB positions and contribute on ST's.
The first to sign elsewhere, I'll say, will be Alan Branch. There's always a market for scheme-versatile run-stuffers his size, and teams will be intrigued by his 2011 season. I expect Jason Jones' injury question marks to prolong his signing as teams do their due dilligence, and as his agent works to negotiate a best offer.