Please don't. TDE and Sterling's other work bear little (if any) resemblance to each other.
I think Sterling's best work is his short fiction and the best of that is in
Crystal Express and
A Good Old-Fashioned Future (though
Globalhead has essential stuff and is very good -
Visionary in Residence is the least of the first four but still has good stuff).
But, if you're looking for novels,
Schismatrix is probably the best place to start. Because the Shaper/Mechanist universe of the novel was first explored in a handful of stories, even if someone wasn't especially interested in short fiction as such, it still might be helpful to read those either in
Crystal Express (where they form the first section, IIRC) or in the later
Schismatrix Plus (which includes just the relevant stories and the novel). I don't think not being familiar with them would hurt anything (the novel is pretty standalone in a plot/character sense, IIRC) but it'd probably be a nice bonus to broaden the picture of the setting (and they're just great stories).
A lot of people regard
Holy Fire highly and might even place it above
Schismatrix but I don't know that I'd agree with that. I have a hard time ranking Sterling's work, though. I lost track of him after 2009* and still haven't read his debut novel,
Involution Ocean, but I've read everything else and, other than
Zeitgeist (really great in ways but really flawed, too) and
The Caryatids (didn't like), I basically like all his solo work.
* Basically, he's only done an ebook-only novel and an expensive small-press collection and some other odds and ends since. Given that his four books from 2000-2009 include the two novels that weren't my favorites and my least favorite collection I haven't been real driven to get later stuff. But his work from c.1980-1999 already puts him safely among the immortals.