You have to take the answers you get with a grain of salt when you ask what's "best" this or that. "Best" is always a matter of personal opinion.
We did our own research before going to Amorgos and thought Aegiali would suit us best. It was in September, which is a bit busier than May in terms of season, but Amorgos is still a peaceful island, unspoiled by crowds of tourists. Here's why we chose Aegiali:
- Aegiali beach (we didn't see a decent beach in Katapola)
- The proximity to several small hilltop villages like Lagada, Potamos, and Tholaria (mainly for hiking, but they're also accessible by car)
- The presence of a renowned diving club
- Accommodation that seemed to match what we were looking for. We stayed here: https://www.amorgosstudios.gr/
As always, I wouldn't say it's the best, just that it suited us.
- And some places like these:
https://maps.app.goo.gl/sm3d1hu58JWaPwVr5
https://maps.app.goo.gl/cmHrpycdsTngqt817
https://maps.app.goo.gl/qxz4dGLGeaaa9DH2A
Since we planned to rent a car and stay for six days, we knew we could explore the other parts of the island anyway. (Katapola, Chora. etc).
Regarding car rental, I chose FM Rent a Car, and it turned out to be an excellent choice. You can pick up and drop off the car at Katapola or Aegiali, which was a plus coming from Santorini since the Seajets ferry only docks at the port of Katapola. The owners are two brothers, each with an office, one in Aegiali and one in Katapola. (Yannis in Aegiali is a nice and funny guy). Just in case:
https://fmrentacaramorgos.gr/
Finally, once on Amorgos, our choice of Aegiali proved to be the right one. In our research, we also found someone who seems like a good option if you want to explore the island with a tour guide: Semeli Drymoniti
https://www.findingreece.com/amorgos-island-experiences/
But we did everything on our own. However you can learn more about Semeli in this video:
https://youtu.be/Vw5FbNAv3Vw?t=1893
This is part of a longer documentary (in 4 parts) about Amorgos
I suggest you do your own research before deciding what your "best" spot will be.