We are a family group of 10 traveling from Girona to BCN for our flight home on Jan 1. Should we take the bus that goes directly to the airport or take the fast train back to Barcelona and then taxi to airport or is it possible to hire a minibus to take us all directly from Girona to BCN? The bus would be the most economical, but I heard there is not much luggage space. Also is it reliable? Would a private transfer if it exists be much more expensive than train fare and multiple taxi fares? Any recommendations would be appreciated .

You can hire a minibus to take you. Depending on where you are staying in Girona, you might have to walk to meet the bus. For 10 people it would be a 16 or 19 passenger bus, most likely, so plenty of room for luggage. I’m not sure what they would charge on a holiday, but I had a transfer from this outfit last year for 250 euros: https://www.minibuses-pacheco.com
They do not speak much English, though. I booked through a travel agency.

This company will be more expensive, because they are not based right in Girona, but they speak English.
https://www.maypebus.com/en/services/transfer/

There are companies based in Barcelona too, it won’t be difficult to find a minibus.

The airport bus from Girona is fine but doesn’t run that often and on January 1st, maybe even less. You can take the train all the way to the airport (the train from Girona then change to the line to the airport) so no need to get taxis from Sants station, but with 10 people that’s a lot of herding.

If you opt for the train, you can change at Barcelona Sants to a airport train. They leave every 30 min from 5.09 until 23.09 (journey time 17 min).

Ask at your hotel in Girona for a recommendation for the transfer. They'll know of several firms and will help you out. E-mail them and they'll probably book it for you.