Category 1: I don't recognize Pearl Necklace, but I all but despise every ZZ Top song I've ever heard. JBH is one of my favorite Foreigner songs. Turn It On Again is one of the better of Genesis' "commercial" songs.
Category 2: Red Barchetta is great. Hold On is really good or great. Brass in Pocket drags this category down. Not a fan of Chrissie Hynde's voice, but it's not a bad song.
Category 3: Mean Street is just ok. I originally liked The Zoo, but it got overplayed, and the live version was beyond tedious. The Stroke is good, but I agree with Stadler that it's probably the 4th best song on Just Say No.
Category 4: Fight the Good Fight is probably my favorite song in any of the categories (a slight edge over Red Barchetta). Hammer to Fall and Twilight Zone are both really good songs.
Category 5: You know there are some good songs in the mix when Children of the Sea is only the third best song. The Hagar song is pretty good. The Waiting is meh (not a Tom Petty fan at all).
It's hard not to vote for Rush, but category 4 has no weak songs and is strongest overall.