Hydra is great but it does take a bit of time and effort to get to from the Cyclades. You’ll need to ferry to Athens, then might have to overnight there, then ferry to Hydra. Whereas Naxos, Paros, Milos, Folegandros, etc. would all be one direct ferry from Santorini or Mykonos. If you do go to Hydra then Leto Hotel is a great choice close to the port and shops and restaurants.
These groups are generally better connected among themselves than with other groups, so you are probably better advised to target them on this basis. As it’s your first time to Greece, you may want the full-on Greek island experience and you could easily fill your five weeks flitting from one island to the other in the Cyclades. You could start in Kea and work your way down to Milos via Kythnos, Serifos and Sifnos then segue to Paros and Naxos. Dip down to Santorini, up to Mykonos and back to Piraeus. The map will also show plenty of other Cyclades islands to pick and choose from such as Ios, Sikinos, Folegandros, Amorgos, Syros, Tinos and Andros – yes! too many choices, but you will find that sticking to one group it will be easier to get between them. Realistically for a period of five weeks you will not want to be doing more than 6-8 islands.