This might be a hot take, but the later Alex Cross novels don't rank as high for me as the originals. The early books had a grittier, more visceral feel, almost like horror-thrillers. The newer ones, while still page-turners, can feel a bit more procedural and reliant on the established formula. For my personal top-tier Patterson thrillers, I'm looking at 'Kiss the Girls', 'Pop Goes the Weasel', and 'Roses Are Red'. They captured Cross at his most driven and the villains at their most chilling. That era is the peak of Patterson's crime writing for my money.
Is there a specific reason you're looking for an order? Are you trying to study the evolution of the modern thriller, or just want some entertaining page-turners for a vacation? If it's the latter, any order works—grab the one with the most intriguing back-cover blurb. If it's the former, then publication order across his entire bibliography is a massive undertaking, but it's the only academic answer.
His shift from solo author to co-author 'producer' model is a key moment in publishing history.
My first was '3rd Degree' from Women's Murder Club. A bombing opens the book, and the investigation threatens one of the club members directly. The personal stakes are immense from page one. What I loved was how the friendship between the women was both a support system and a vulnerability the killer could exploit. It has all the investigative pieces but makes you care deeply about the people solving the case. That emotional core is what makes the series so enduring for me.
The order I recommend is based on peak quality, not chronology. Start with 'Kiss the Girls' (Alex Cross #2). It's arguably the high point of the series and works well enough as a standalone. If you love it, go back to 'Along Came a Spider'. If you think it's just okay, maybe try a standalone next. Why start with #2? Because if you start with #1 and aren't impressed, you might miss the better book. This is a controversial take, but for a skeptic, it's the best test drive. Maximum impact right out of the gate.