I've just started reading these books; so far I've read The Phoenix Guards and the first three books in publication order (Jhereg and two others).
Most people seem to recommend reading them in order of publication date, but I'm going to buck the trend a little: if I'd started with Jhereg, I probably wouldn't have bothered reading any of the others. I mean, it's not a bad novel, but nothing in it particularly grabbed me: it read like most other run-of-the-mill fantasies, as far as I was concerned. The Phoenix Guards, on the other hand, is written in a playfully florid prose that I really enjoyed.
If you read them in publication order, you're going to be starting with the clumsier, early-novelist works. I'd recommend starting with something from a later time period, when Brust has found his footing as a writer.
This will mean that a lot of the world of The Phoenix Guards won't make much sense, but if you just go with the flow, it's not too bad.
Daniel