VESSELS -- I would recommend taking a CAR FERRY (conventional large ferry (1200-1600 psgr capacity, often 1/3 full offseason); these have several passenger decks + a vehicle deck, cafes, corridors, like a small ship really. The other option is a Catamaran. a bit faster but resrved economy seats about 2x as expensive. Some have vehicle decks but carry 400-500 psgr all-resrved seats , no outside deck to walk on, no corridors... and for a 4.5+ hour journey its confining. PLUS in October, winds can make these 'rocky"
PORT of RAFINA -- Look at a Map. IF your destination is Monastiraki, Rafina can take much longer. Either a city bus from Port (with a gajillion stops) or a bus to Airport (infrequent, 40 minutes) and from there you STILL have to reach Athens. options are:
(1) taxi flat rate €38 div by 4 = not bad,
(2) Car Service Welcome Pickups - €38-42 - https://www.welcomepickups.com
(3) X95 Express BUS to Central ATH, €6 each, no pickpocket hazard, I usually take this one ... BUT terminates @ Syntagma Square & you'd have to roll your bags at least 8 blocks to Monastiraki Square and it's a hike I can attest.
(4) METRO -- €8 ?each -- This Goes from Airport to Monastiraki ... BUT -- With a bunch of luggage and unfamiliarity with public transit (unless u are subway vets from NY, Chi, Philly, and I'm guessing not) Beware!.... these lines are targeted by skilled pickpockets (mainly Albanians) who jostle & bump tourists unused to crowded trains & theft occurs during confusion. At Monastiraki there's an escalator up from underground -- but that escalator is where my friend had his billfold lifted from his pants pocket where he was foolishly keeping it (btw 75% of pickpocket victms are men who persist in keeping valuables in pockets).
PORT OF PIRAEUS --
(1) METRO - Mykonos Pier only 200 yards from GREEN LINE, €2 ? each -- stops at Monastiraki station which would be a short walk to your hotel BUT see above pickpocket warnings
(2) TAXI - No flat-fee but €25 should be ample; don't try to hail on street, get one AT pier line & ascertain fare before entering.
(3) CAR SERVICE - Welcome Pickups is well-reviewed, --can be booked before trip or via phone/email during trip -- pre-set fare i n advance; should not be more than than €40 I am sure.
So... my recommend would be a conventional Ferry to PIREAUS (there's one @ 8 am & about ? 2:30pm? -- and your transport from there depends on your budgeteering impulses and Metro bravado.