I have no comments or suggestions about Crete; it's been over 30 years since I've been there, but after several stays totaling a few weeks exploring Paros and Naxos, I honestly can't recommend one island over the other. There are similarities and also differences that only become apparent after a more prolonged visit..
Both islands have airports, making them among the top 5 most crowded islands in the Cyclades.
Naxos is larger and mountainous than Paros, but to truly enjoy it, you need to do more than just stay in Naxos Town spending most of your time on the surrounding beaches. The same is true for Paros if you only stay in Parikia or Naoussa. Going to Paros also allows you to visit Antiparos its chic little neighbor. As for shopping, I can’t comment much as we only pickup essentials like food and drinks at local supermarkets.
Anyway, you can just as easily choose any of the other 20 Cycladic islands and won't be disappointed by either if you rent a car and have enough time to explore them.
We also stayed in Milos, it's not our favorite island. There are no villages other than the capital and its neighbor Chora, and Pollonia in the far north. It’s mainly famous for Sarakiniko, a volcanic beach that attracts a lot of social media attention. Almost half of Milos is a Natura 2000 protected area, practically deserted and only accessible with a four-wheel-drive vehicle. You may also encounter difficulties getting to or from Paros/Naxos by ferry from Milos. Milos is in the western Cyclades and is not on the same ferry routes.
However, the small island of Kimolos, accessible from Pollonia, is worth discovering if you are seeking a place away from the hustle of mass tourism.