No. 1 budget free agent the LA Angels should definitely pursue after the lockout: Joe Kelly
Here's why I have Joe Kelly listed as a "budget free agent" for the taking for the LA Angels: He may take a while to get signed when the lockout ends. Kelly is a very good reliever, but he's not going to be as sought after as the Kenley Jansen's of the free agent class, or the Brad Hand's. He's not as good as some of the best of the best arms in this class.
He also doesn't close, so that may not be as attractive to teams. We have to remember that the longer he takes to get signed is the less value he has on the market. Therefore, it's possible Kelly could go for cheaper, especially when like Bradley (and Diekman for that matter), he didn't have as good of a year last year as he did the year before.
There IS a chance they could sign Kelly late for a bargain. It's not as likely as the Angels acquiring the other two, but there's a chance. Regardless, they need to upgrade the bullpen, and free agency is likely to be the easiest (and maybe cheapest) way to do it.