Sequence is very important when island hopping. You will want to do your first island closest to Athens or furthest from Athens.
Ios is furthest and Mykonos is closest.
Paros is in the middle. I would be tempted to ferry from Rafina port to Mykonos. There are several ferries that do Mykonos to Paros. Because every ferry hop uses up a minimum of half a day we always book the ferry that gets us to our next island the quickest. I suspect that will be one of the Championjets or possibly Hellenic seaways.
Paros to Antiparos is a 7 minute ferry ride plus a bus to the ferry or you can just take a water taxi from the ferry port to Antiparos. Its about 15 minutes and was about 15 euros a few years ago. You can do Antiparos as a day trip but it is also very nice for a few night stay.
Then do Paros to Ios. There are several ferries that do this route.
Now what do you want to do after Ios. You can ferry back to Paros and fly from there, or take the ferry to Santorini and fly from there.
If you opt for the ferry back to Athens it will probably take 5 to 6 hours.
Hope that makes sense.