We are staying in the Rue Cler area. Our hotel offers a shuttle service for 20 euro per person for the trip from the airport and the trip to the airport. Is this a good deal or is there a better/cheaper way?
If you're packing light and can easily schlepp your own luggage, then "better" and "cheaper" can go together. Take the RER B to Gare du Nord, metro line 4 to Strasbourg-St-Denis, and metro line 8 to either La Tour Maubourg or Ecole Militaire (whichever station is closer to your hotel). See the Paris by Train site. The fare is €8.50.
A taxi will cost around €50. So the shuttle would be cheaper for a party of two but more expensive for a party of three.
From Rue Cler you can take metro to airport bus to CDG, it is long with changes and hauling luggage (prob about 10euros) yes cheaper but not very convenient. IMO I would take the hotel shuttle offered if only 20 e p/p rdtrip, sounds like a great deal.