I always thought this was a super straightforward answer, but then I realized it's actually a bit of a can of worms. For the 'Empire' books specifically - 'Pebble in the Sky', 'The Stars, Like Dust', and 'Currents of Space' - the internal chronology doesn't match the publication order at all, and they're largely standalone anyway. I'd honestly just read them in publication order: 'Pebble', 'The Stars', then 'Currents'. That sequence shows you how Asimov's ideas about the universe evolved. 'Pebble' feels a lot rougher and more pulpy, but it has this weird, paranoid energy I love.
That said, if you're reading them as part of the whole 'Foundation' mega-series, the order gets totally bonkers. Some people will tell you to read them chronologically within the in-universe timeline, which would slot them in between the Robots and Foundation stories. I tried that once and it felt disjointed, like jumping between completely different eras of sci-fi writing. The 'Empire' books are so tonally different from the 'Foundation' trilogy - less grand political psychohistory, more adventure-of-the-week. I'd treat them as a separate, earlier trilogy you can enjoy on its own terms.
I read 'The Stars, Like Dust' last, and honestly, I'm glad I did. It's the weakest of the three for me, with a plot that feels a bit thin and rushed. If I'd started with that one, I might not have continued.