I suggest a taxi to the hotel on arrival, from the official taxi line in front of the terminal (not from someone who approaches you offering a ride). Have the hotel name and address on a piece of paper to show the driver if necessary. It's a fixed fare, I don't know how much but someone else will. Tipping not necessary unless the driver gives extra-good service.
For travel in the city I suggest the Navigo Decouverte pass, costing 27.80 euros for a week's unlimited bus, RER, tram and Metro travel. This will probably pay for itself in a few days. You'll need to bring or get a photo (see the link). The week it covers starts Monday morning, perfect for your schedule. Hopefully you'll have some good weather when you'll want to walk, but the pass will make it easy to ride, even short distances or on-and-off along bus lines like you describe.
Also consider the Paris Museum Pass, admitting you to many museums and other sights (but not Eiffel Tower) for as many consecutive days as you buy. You can get this at any participating museum or elsewhere. This pass used to cover as many visits as you wanted to any covered museum, but now I understand it's just one visit per museum. Also the Louvre now requires a timed entry ticket, which isn't meshing well with the Museum Pass. But this may not be a problem in December.
Bring layers of clothing, a waterproof outer layer, a warm hat, sturdy shoes that will keep your feet as dry as possible, and wool or similar socks. Fleece and Gore-Tex are great, polypropylene underwear, wool is good, cotton not so useful.