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.
I'm going to go against the grain and say start with the middle. Seriously. Pick up 'Pop Goes the Weasel' (Alex Cross #9) or 'The 6th Target' (Women's Murder Club #6). If you can enjoy a Patterson book plopped into an ongoing storyline and still get hooked, you'll know his formula works for you. Then you can go back and explore the earlier books to fill in the blanks. It's a fun experiment that removes the pressure of 'starting a journey.' These books are designed to be accessible, so you rarely feel completely adrift.
The audiobook of 'The President Is Missing' read by Dennis Quaid (and others) was a whole production. That kind of star power in the narration draws in listeners who might otherwise skip it. It's another example of how a book's popularity can be amplified by its presentation in other media formats.
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.