The box set remixes are mostly improvements over the original mixes, or perhaps it's the cleaned-up production as well. Genesis, especially early Genesis, had a lot of layered sound. Acoustic guitars, keyboards, all mixed into a backdrop for Peter Gabriel's vocals. It's nice hearing each of the parts more clearly. Where I have a bit of a problem is with the first "Phil era" box. '76 Genesis (the two without Peter but still with Steve Hackett) kept a lot of layering, maybe even did more of it, but there was still a very dynamic element to the music that I feel got lost in the remixes. Yeah, I like hearing all the parts, but some parts were meant to be softer or louder than others, not everything the same volume. That's part of the arrangement as well.
Nursery Cryme is a good starting point because both Phil Collins and Steve Hackett joined on that album, making it the first "classic five-piece" album.
Foxtrot is also a good starting point because it's the next album, and the writing had matured a bit. It also contains the band's magnum opus, "Supper's Ready".
A Trick of the Tail is a good starting point because it was the first album after Peter left, but the band still had a somewhat proggy sensibility. The arrangements are simpler, but there are some nice instrumental passages.
Wind & Wuthering was the follow-up, the other four-piece album and, similar to how Foxtrot builds upon Nursery Cryme, Wind & Wuthering finds the four-piece band stretching out a bit and getting a little more proggy. It is also the mellowist Genesis album overall (not counting Trespass), so it's proggy, but pretty chill. Lots of instrumental.
So basically either of the first two from the Gabriel era, or the first two from the Gabriel-less era. If you can afford the box sets, they're great values and perfectly good for building a collection quickly, so either of the first two boxes would also be great. I bought them both and like them both.