Here's the sad truth:
For all the frenzy surrounding it, there's very little your favorite NFL team can do in free agency to make any kind of difference. This is because free agency, as the NFL defines it, stinks. And by "stinks", I mean that it is so heavily slanted toward preserving the sanctity of owners' pocketbooks (and protecting them from their uncontrollable urge to spend like a drunken grandmother at Filene's the night before Hanukkah) that it does very little for either the players or the teams that it's supposed to benefit.
Look, the thing with NFL free agency is that it takes for-freaking-ever to get to it, and NFL careers are generally brutal and short. By the time a player reaches free agency, his tires are going to have a ton of mileage on them. That's just the way it is; to play football is to absorb hits, and to absorb hits is to have yourself be physically broken down. There's a reason most running backs are done by the time they're 30 - it's all the punishment they take - and by some odd coincidence, that's roughly when most of them hit free agency for the first time.
Then there's the fact that by definition, most free agents are guys their old teams didn't want. Maybe they lost a step. Maybe they were making too much money for their production. Maybe they were making too much money for their team's cap. And maybe they were signed to a previous free agent deal that was backloaded with dollars that everyone knew would never get paid out. In any case, these are guys who weren't worth it to their previous employers any more. They might have big names - Julius Peppers, I'm looking at you. They might have a special place in your memories - yes, Jason Avant, Philly will always love you. But they weren't getting the job done well enough to stick around.
And yes, there are a few big name guys who are still theoretically at the top of their game who get out there, but they're few and far between, and for every Peyton Manning, there's a ton of Matt Cassels and Matt Flynns and late career Matt Hasselbecks and other guys named Matt. A lot of times the "big names" are just the biggest names available, as if it's a zero-sum game on excitement and there's a certain amount of hype that has to go somewhere.
So, sure, your favorite team can help themselves through free agency. It's fun to dream on what Darren Sproles will do in a Chip Kelly offense (best guess: replace LeSean McCoy after he wears down from overwork). But anyone worrying that the Denver Broncos just locked up the next fourteen Super Bowls because they locked down a bunch of guys who had priced themselves out of their previous jobs or contracts can probably relax a little. Because free agency may look like it's about helping teams get better, but really, it's more flea market than auction.