does anyone have any general recommendations regarding this ferry? I think I know how to get from my hostel in Rome to the ferry departure. However, I'm unsure about things like:

-I'll have a big backpack and daypack, can I store my big pack so I don't have to worry about it?
-If I have a "pullman seat", is there a place to lay out or sleep?
-Is it smart to buy the meals or just bring my own food?

Thanks for any words of advice.

You would take the train from Rome to Civitavecchia (less than 10€). I've only had cabins on overnight ferries, but if you are asking about Grimaldi Lines, there are pictures of the pullman seats if you click on fleet.
http://www.grimaldi-lines.com/england/index.jsp?lan=EN

This about luggage from Grimaldi's terms:
LUGGAGE
Only personal belongings are allowed to be carried in the passenger’s luggage. In particular the passenger’s luggage shall not include goods carried for commercial purposes. No dangerous and hazardous goods are allowed. (Dangerous and hazardous goods include, but are not limited to: arms, explosives, illegal drugs).
Passengers are invited to take with them the luggage necessary for the crossing; the garage will not be accessible while the vessel is at sea.
Cabin passengers are allowed one suitcase per person. Passenger travelling in Pullman Seat or as Deck Passenger are allowed only one hand luggage of reduced size. All other luggage, unless stored in or on top of the vehicle, has to be deposited, against payment, in the vessel’s baggage storage room.
Household good and other heavy items have to be check-in and are carried in the garage (paying)
The Carrier’s liability for luggage does not exceed the limit imposed by the Italian Code of Navigation or, if applicable, by an International Convention, and only within the limit of 30 kg of non registered luggage per person, including luggage carried inside or on top of the vehicle or in the vessel’s luggage room.

Thanks. So does that mean I can take my big backpack and store it in their storage room, then carry my daypack to my seat? I'm assuming their would be a fee for storing luggage. Is that what it means by saying "against payment"?

No idea what luggage fees are, but I'm sure you could e-mail and ask.

It might be cheaper to fly unless you are using a railpass (some include a discount on this ferry). Ryan Air flies Rome Ciampino to Barcelona and Girona and Vueling flies Rome FCO to Barcelona.

www.skyscanner.net
www.whichbudget.com

for anybody who might care, the Grimaldi lines ferries between Civitavecchia and Barcelona are the largest/heaviest Italian-flagged ferry ships in the Mediterranean (and quite new).