I haven’t read “The Genome”, but Sergei Lukyanenko’s Nightwatch/Daywatch/etc. series are great fun. Michael Swanwick is usually solid (though I’m not sure why MaryAnne from Gilligan’s Island is on the cover of that book).
In the second set, John Brunner is one of the most important writers of the 70s, though if you haven’t read him at all I’d recommendeither “The Sheep Look Up” or “Stand on Zanzibar” first. And of course Andre Norton is Andre Norton.
The third set has several excellent choices in it, and would be worth buying just for “Dawn” if you haven’t read Butler.
And of course the 4th set has both Haldeman and Anderson in it. Not their best work, but certainly both good reading.