If you are flying from the US probably you will be landing at CDG, but if you can get a flight to Orly that is cheaper and closer to town.
A taxi is your absolutely best bet on arrival with luggage. 3 people ride for about 30-35 Euros from Orly to the center and about 50-55 from CDG. Public transport from Orly for 3 is about 36 Euro. It is 10 a head from CDG on the train. And with the train you have to lug bags up and down stairs and are very vulnerable to pickpockets with all your stuff.
On arrival at CDG all 6 of you should go to the taxi queue (don't accept offers from anyone who approaches you, these are major scammsters) Have one person let the dispatcher know that there are 6 of you, pointing to your group in line. Then wait your turn and the dispatcher will match you with a van type can that can take all 6 and your luggage. The cost will be the meter (about 50-55) plus 3 Euro for each of the 4-6th passengers and one Euro for each bag in the trunk past 1 -- so my guess would be about 65 Euro for your group, maybe 70. It would be 60 to take the train.
The train is great once you are settled in, but a taxi is best on arrival especially with several people.
What an exiting trip -- have a marvelous time in Paris.