I've read the entire series, and I highly recommend reading them all in order! It's a shared world in the sense that each book is written by multiple authors. However, each book still builds upon the previous one. If you read out of order you're likely to not understand as well, feel less connected to the characters and trip over spoilers.
However, if you must read the books piecemeal, it's useful to know that the stories do tend to have a break in continuity whenever the series changed publisher. See the Wild Cards Wikipedia page for the full list of books by publisher.
So the first twelve books published by Bantam evolve continuously and have a lot of shared characters, with plots often spanning over several books. It starts with the Astronomer and finishes with Bloat and the Jumpers as far as I recall.
The next three published by Baen are hard to find, but worth reading. They form a 3-book plot about the Black Trump.
The ibooks pair of books I don't remember so well, but I think it was the John Fortune plotline. These two books stand together.
Finally, Tor rebooted the series with the American Hero plotline, with the last book in this series being High Stakes and more books planned.
I hope that helps!