You really should be asking those question (not taxi cost) of your cruise line. There is a cruise port at the bottom of Las Ramblas but in four trips to Barcelona we have only docked there once. If your cruise originate there then it is most likely you would be using that port but double check to make sure. Supplements are extra charges, generally for luggage - say - 2 Euro per bag as an example, night time surcharges, etc. Our experience in other beginning ports is that the taxi "might" have a flat rate to the cruise port - generally not a deal but much better than the ship's transport. Establish all your prices BEFORE getting into the cab.
On this site you will get the general recommendation of packing light which you should consider. Our total luggage for cruises is three carry-on size bags (two rolling, one backpack style) so I know it can be done. Our first cruise was well above that and handling the luggage was a disaster. Never again.
If you sign up for your ship on Cruisecritic.com you will get better responses related to your specific cruise. If you don't have too much luggage you might be able to share a taxi with another couple.