??
Cake has been around about as long as some of the bands you called ‘older’. I think they even predate Cracker (though CvB goes back to before Cracker, even if it’s not quite the same band).
Cake’s first album, Motorcade of Generosity, was released in 1994.
Which is the same year Cracker’s Kerosene Hat was a big hit. Cake had a song on the radio before that (so did Cracker). Incidentally also when The Offspring finally broke through with Smash.
Checking Wikipedia - Rancid, Belly, Cake, and Cracker were all formed in 1991. About the only distinction is that the members of Cake were not in any well-known prior acts. All of which may be worth checking out by the OP ( Operation Ivy, Dance Hall Crashers, The Breeders, and Camper van Beethoven).
I’d vote for Authority Zero. Most of the other bands mentioned don’t remotely have the ska-skate rhythm going on (even though its influence in Offspring’s music is minimal sometimes.)
Not that I don’t like the bands mentioned, in fact I like most of them more than Authority Zero. But rhythmically they sound very similar to Offspring.
And the Descendents. That’'s about the only one I can think of that hasn’t been named yet.
A hint about getting into punk: independent labels tend to be very consistent as to sound. If you like one band on a certain label, you are apt to like most of the rest of their offerings. This isn’t always true, but it’s a good thing to keep in mind.
Oh, and check out Me First and the Gimme Gimmes. They’re sort of a pop punk super group (pop punk in this case meaning NOFX, Screeching Weasel, that sort of specific subgenre, not just punk on pop radio) that covers mainstream hits.
I chalk it up to a bad memory and my oscillating between different kinds of music. For example, since early '09, I listen almost exclusively to hip hop. Prior to that, it was alternative rock for about 3 years. Prior to that, I simply got bored with music for a few years and listened only to sports radio and conservative talk radio (which pretty much got me angry every day). Hip hop before that; Brit pop/alternative before that…etc.