Here's my attempt:
I started off taking one track from each album
The Knife (because it's the only track from Trespass that I know)
The Musical Box (I don't have Nursery Cryme either
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)
Supper's Ready (on a best of Genesis, you cannot leave this one out)
Dancing With the Moonlit Knight (mainly because it wasn't on The Platinum Collection)
The Lamb Lies Down on Broadway (I've only heard the Lamb a few times, and this was the first song that came to mind)
Squonk (for the same reason as Dancing...)
Afterglow (yet another Genesis album I need to get)
Undertow (ditto)
That left me with 5 minutes and 14 seconds, so as a final song I chose
"The Carpet Crawlers" (it takes the total length to 75:01, but I'm sure
that would be OK).