I bounced around the series myself, started with 'The Hot Zone' which is technically non-fiction but everyone treats it as the intro. That one's a standalone, but it sets the tone for the Preston-verse—the meticulous, almost thriller-like approach to science. After that, I'd hit 'The Cobra Event'. It's a novel, but it reads like a natural progression from 'The Hot Zone', taking that bio-terror fear and cranking it into a fiction scenario.
From there, you can kinda go anywhere. 'Demon in the Freezer' and 'The Panic Virus' are more great non-fiction deep dives into specific topics. I don't think there's a strict 'series order' because they're mostly thematically linked, not a continuous story. Reading 'The Hot Zone' first just gives you the foundational awe (and terror) that colors everything else he writes.