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.
Forget series versus standalones. The true top-selling 'book' might be one of the early 'Alex Cross' novels that has been in print for 30 years and sold steadily every single week since publication. 'Kiss the Girls' or 'Along Came a Spider' have a cumulative sales tally that a new release, even a huge one, can't match in a single year. The long-tail sales of those foundational books are monstrous. So while we debate which new release hits #1, the all-time champion is probably sitting quietly in the backlist, selling thousands of copies a week to new readers discovering Patterson for the first time.
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.