The port of Piraeus is very large (4 km of quays from one end to another). And Piraeus is a big city too. Given all the possibilities of transport from the airport or from Athens it is difficult to say which is the best transport without knowing the final destination in Piraeus.
Since you are going to Paros, your ferry will leave from a Gate located between Gate E6 and Gate E9.
If it's a Blue Star Ferry, it will be at Gate E6. If it's a Seajets it'll probably be at Gate E9.
From the metro/train station Gate E6 is very close (less than 10
minute walk)
Seajets Gate E9 is further away (15 to 20 minutes walk)
The X96 bus that comes from the airport stops at several bus stops in the port. For someone who does not know Piraeus it can be difficult to determine at which bus stop to get off.
I think that now, like in all other buses in Athens, there is an electronic display in the bus which indicates in real time its position and the next stop (I haven't taken the X96 for more than 4 years)
But if he waits to arrive at the bus terminus to get off, he will be at the end of the port and will have to walk back (which can take more than 30 minutes on foot).
Also, depending on the traffic and the time, the bus journey can last more than an hour (sometimes 1h20).
The advantage of the bus is that it operates 24/7 and is not expensive (less than €6)
In my opinion and as I have tried everything in the last 20 years since the new airport exists, from the airport I would recommend the metro or the suburban train.
The train leaves the airport at 07 of every hour between 06:07 and 23:07. He arrives at the port of Piraeus 63 minutes later.
The metro leaves every half hour at 02 and 32
it takes 40 minutes to Monastiraki station where you have to get off to take the line that goes to Piraeus. Travel time Monastiraki - Piraeus is about 15 minutes.
(Unless the new stations are open, as I specified in a previous message. In this case the route will be direct)
Train and metro leave from the same platforms at the airport station. The ticket price is 9€
The station in Piraeus is also the same for the train and metro
The metro is also the best option from the center of Athens. There are also buses and trolleybuses, but I will not complicate the subject. You have enough to digest for today LoL