Which ferry company

You'll see Santorini from all the ferries. The best option is to take a traditional Blue Star ferry (Blue Star 1 or Blue Star Delos).

They are: more stable, more comfortable, the decks are equipped with chairs and tables, they have shaded areas, and there are places relatively sheltered from the wind. They are also slower, so technically you'll enjoy the view of Santorini for longer. The downside is that the journey to Athens takes 8 to 9 hours.

All the Seajets ferries (those with "Champion" in the name) are faster, much more expensive, and less stable. The trip to Athens takes about 5.5 hours. The decks are just some kind of unequipped terrace (no chairs, no tables) about the size of half a tennis court. There's no way to sit down or shelter from the wind, they sail at a speed of about 45 knots (52 mph), so you'll get plenty of wind.

The conventional ferries (Blue Star Ferries, Fast Ferries) are the only ones that go through the Caldera and thus offer the best views of Santorini. The highspeed ferries go around the islands (Palia, Tholos & Thirassia) in front of Santorini which obstructs the view.
The trip duration of the conventional ferries can vary a lot depending the ferry.
As mentioned by JoLui it's about 8 hours with the daily Blue Star Delos (or Blue Star 1) that goes via Naxos and Paros. However if you go on a Friday morning with the Blue Star Chios it only takes 5,5 hours because this one goes directly to Piraeus without stops in between.
If you like a daycruise of some 10 hours through the Aegean with several stops at other islands, take the Dionisios Solomos from Fast Ferries which goes 3 times a week. Between Santorini and Piraeus this ferry stops in Ios, Sikinos, Folegandros, Kimolos or Milos (depending the day), Sifnos and Serifos. Some days also in Kythnos before reaching Piraeus.

Thank you all for the good information.

If you have the time and are interested in visiting some islands the next few years, I can totally recommend the mentioned trip by Nicksy (with Fast Ferries) It takes ages, but you get a quick short impression of many islands and the urge to visit all of them will definitely grow :-)

Thank you for your information. When they stop at the other islands on the way to Athens, is there time to get off and explore?

Is it time to get off and explore?

Definitely not! The ferry departs the island immediately after all passengers and vehicles have disembarked and new ones are on board. It's very, very quick. Just a few minutes.

https://youtu.be/dFlfiqE67nk?t=277

Depending on the amount of traffic going on and off the ferry, these stops take between 5 and 15 minutes. Mind you there won't be that much people on that specific ferry as you see on the video linked bu JoLui.
This is how the trip goes:
Leave from Santorini and sail at reduced speed through the Caldera.
First stop is Ios where you enter in a natural bay to get to the port. From the ferry you will have a nice view of the old chora with the white houses on the hill.
From Ios to Sikinos takes only 20 minutes. The stop in Sikinos takes not long as it is probably the Cycladic island with the least tourism. Last year when we arrived there in May with the ferry from Naxos we were the only 2 tourists disembarking. Besides the port there is only one other village. It's the main village situated on the other side of the island and from the ferry you can see it on the top of the hills.
Next is Folegandros. It has become more and more popular the last few years and there will be more passengers here. After leaving Folegandros and sailing along the cliffs you can see the houses of Chora right up to the edge of the cliffs.
Between Folegandros and Kimolos the ferry passes Poliegos, the biggest uninhabited island in Greece. If the ferry has a stop in Kimolos, just like in Sikinos it won't be a long one
(Again) If there is a stop in Milos that could probably be the longest one on the trip. Milos has become as popular as Naxos and Paros the last few years so probably more passengers on and off there. All though many tourist prefer the (expensive) highspeed ferries from Milos to Piraeus.
About an hour after Milos comes Sifnos, an island known for his food and hiking trails. And again an hour later is a stop at Serifos, very popular with Athenians for a weekend stay.
On certain days there is also a stop in Kythnos before going to the finish in Piraeus.
Santorini to Piraeus is 48 Euro for an economy ticket, 50 Euro for a reserved airseat (reclining seat). Not bad for a 10 hour cruise in the Aegean.
Btw, the ferry is named after the poet Dionysios Solomos who wrote the text of the Greek national hymn.