I started with Jazz Stubby 2.0mm about 27-28 years ago. Used them for over 20 years, then I started looking for something different. I tried some faux turtle shell picks from Red Bear. The first one was amazing, and it lasted over a year (for ~$28, it better), but they’re handmade, and none of the replacements I bought were as good as the first one, so I stopped and looked for something more dependable.
I went to the carbon fiber max-grips, and found they felt great, and the riffing was spectacular, but there was too much pick noise for lead playing. I then bought a dunlop sampler, and it was a close match between the yellowish Ultex and the John Petrucci signature picks. In the end, I stayed with the Ultex – they feel great, have some good grip to them, last a long-ass time, and sound just right.
Every single pick through that whole process was a Jazz-style pick, and I stayed there. Some people are surprised I can do light strumming and relaxed-sounding playing with it, but it just feels natural to me. All a matter of personal taste.
The JPs are ultex, too, and size-wise, they are slightly larger than a jazz III, but not even close to a standard-size pick. If the Jazz feels a little too small you to, try the JPs.
Good luck on your pick journey!