Ferry purchase on-line vs. waiting to purchase in Greece

It is certainly not an advantage to purchase your ferry tickets on line and in advance. Even if you decide to do that you have to go to the kiosk at the port to pick up your tickets. So you really are not getting an advantage by booking ahead. If you choose to book ahead anyway then my advice is to find your preferred ferry time, price, then book the tickets directly on that ferry companys web site.

We always wait until we are in Greece before we book our ferry tickets. We go to a local travel agent ( any one will do) and ask about the best way to get to the next island. They will know of strikes and weather patterns and schedule changes. Buy your ticket on the island. Now you will have a physical ticket and you don't have to stop at the kiosk.

Advantage of using the conventional ferries over high speed boats.
Depends.
A slow conventional ferry gives you lots of deck space to be out for the views. In particular the trip in the caldera is spectacular. They are way less expensive than fast ferries. They are very stable.
Fast Ferries
Some of the fast ferries have open decks so you get about 15 minutes of view time versus at least a half hour on the conventional ferries. The open deck ships I am referring to are Seajets Championjet 1 and 2. They do not appear to be servicing either of your island hops so it appears you will be cooped up inside for the whole trip. Small fast cats can be bouncy in rough seas but on normal days they are a smooth sail.
For me the most valuable commodity on a Greek trip is not cost but rather efficiency. Every island hop basically uses a half day when you include check out, get to port, wait for ferry, take the trip then book into your next hotel. Even the short 1 hour hop from Paros to Naxos actually saw us on the beach in Naxos at 3 in the afternoon.

I always book a fast ferry as long as it gets me to my next island the fastest.
When to arrive in port.
Generally speaking you should be in port within an hour of sailing. The advantage of having purchased your ticket at the travel agent means you can arrive closer to sailing time but I always give ourselves an hour or so.
The port at Santorini is serviced by a switchback steep road. Its quite the experience to see it however it is often bottle necked and can take a good half hour to get down to the port. You need to be aware of that when planning you timing and hotel check out.

Stanbr is right on. I'd add there will always be room on the large ferries. Except maybe for the August 15 religious holiday. I have no experience on the fast ferrys.

Our experience last year in Santorini was the bus left Fira about 1 hour before ferry arrival/departure. We missed the bus due to last minute shopping and took a taxi instead for 20 Euro to the new port. During high season, the bus may fill up and not have anymore standing room.

We had gotten all our ferry tickets at our first island. When we decided to change our ferry, it was only 1.5 Euro per ticket to make that change. You can use any tour/ferry shop in town.