You will probably have to fly to Athens. I just did a search for Santorini to Rome and there are no direct flights on October 28. So that means you are probably going to have to fly in and out of Athens.
Most experienced travelers like to get out to their furthest island immediately on arrival in Athens. We take the first connecting flight and leave Athens to the end of the trip. It appears you are interested in Santorini Naxos Milos and possibly Paros.
Sequence is important when island hopping and every hop eats up a minimum of half a day. Fortunately you have lots of time.
Options
Crete may be a consideration for you. It has lots of Ancient sites Minoen to Venetian to Roman. It has great beaches. And it is so large that you can easily spend two weeks there and just visit the west. It is relatively inexpensive for hotels and dining and can be done on a modest budget. Transportation by local bus is cheap and reliable.
Western Crete http://www.flickr.com/photos/stanbr54/sets/72157632115757899/
Aptera images 38-62 Balos Gramovossa images 79-106
Crete Archeological sites https://www.flickr.com/photos/stanbr54/sets/72157645085297380/
2017 Crete Archeological sites. https://www.flickr.com/photos/stanbr54/albums/72157691001013665
There are several daily ferries from Heraklion to Santorini which takes about 2 to 2.5 hours. Santorini is expensive for food and hotels but It is amazing for its caldera views. This is the place to splurge and get a hotel with Caldera views. Probably three nights is enough.
Santorini http://www.flickr.com/photos/stanbr54/sets/72157632154800782/
If you have chosen to do Crete then you probably will want to fly from Santorini and end your trip in Athens. Three or 4 days in Athens is enough to see the major sites. get a hotel near the Acropolis and everything important will be within walking distance.
Athens http://www.flickr.com/photos/stanbr54/sets/72157632121475515/
If you have not chosen Crete then fly to Santorini or Milos. If you really want to do Milos you have to plan carefully. Its not on the regular Cyclades ferry routes. As far as I can see there is only one ferry a day from Milos to Naxos and that takes about 6 hours. So if you can get a flight fly to Milos first. Milos will be fairly quiet at this time of year as the season winds down quickly after August
Milos http://www.flickr.com/photos/stanbr54/sets/72157632109429236/
Spend your time in Milos then take a ferry to Santorini. There are more ferry choices on that route. From Santorini there are lots of ferries that do the Ios, Naxos, Paros routes. Naxos is our favourite island and needs a minimum of a week and you won't be able to see all it has to offer. 10 days would be even better. Stay at St George beach. Its part of Naxos town so you get a beach vacation with all the activities of town. All of this just a 10 minute stroll along the shore to Naxos town waterfront promenade. Naxos has a smattering of antiquities, great beaches, hikes and mountain villages where you can see what life in Greece was like in the past. You can also take day excursion boats to Delos Mykonos or the small Cyclades islands. Of course Paros is equally as nice so you can do both in two hops or just concentrate on one.
Naxos Mountains and Villages http://www.flickr.com/photos/stanbr54/sets/72157632110674306/
Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/
Trip around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/
Fly back to Athens for the end of your trip. There are no inter island flight to these islands it has to be done by ferry but all of them have flights to Athens.
Hope that helps