First: Welcome to the DIS!!!!
We prefer the Magic Kingdom resorts, especially if you are travelling with young children or if you plan to spend a lot of time in the Magic Kingdom. The two MK resorts that you mention are both on the monorail line and the best transportation options of any other resort in WDW! Both are spectacular resorts that offer amazing, but very different, experiences.
If, like happy mommy, you prefer to have everything under one roof, then the Contemporary (CR) with a tower room is an excellent choice. The Poly has a separate longhouse for shops and restaurants with all the rooms scattered about the resort in other longhouses or bungalows.
Which is more important to you, your room or the grounds of the resort?
At the Poly you will have lovely grounds to walk around with a beautifully themed main pool and a beach area from which to watch Wishes fireworks. It is so romantic and relaxing. The atmosphere and theming of this resort is perfect! It is the favourite resort of many, many WDW resort guests at least partially because of the wonderful effect of staying in this relaxing setting. LOVELY! OTOH, There may be some construction on the east pool, however, during your stay. It may be finished or nearly finished by January, but it is worth knowing about the possibility. The large rooms here are comfortable and gorgeous. The only potential problem(s) are: 1. some rooms (about 1/3) do not have balconies and 2. some rooms have less desirable views and 3. construction may result in daytime noise (important if you have napping children).
At the CR you will have large comfortable rooms. If you book the tower, you will have a large balcony with a spectacular view of either Bay Lake (SV) or the entire MK area (TPV). The view from the TPV rooms in the tower is nothing short of wonderful. When you enter the room it is all you can see - the panoramic view of EVERYTHING! If you book the garden wing you will either have a garden view (Grounds or pool) or a standard view (parking lot). Also, in the garden wing, the rooms do not have balconies. Ground floor rooms have patios, but the second and third floor rooms have a sliding glass door that opens onto a railing but no balcony. The grounds at the CR less expansive and are open, with less foliage than at the Poly. The pools are simple with no real theming evident. The pools are rarely crowded and have a nice slide, though, and are situated with a very nice view of Bay Lake. The potential problems at this resort are:1. the theme here doesn't feel like a theme because it is so much like any hotel in North America, especially in its public spaces and 2. standard view rooms have less desirable views and 3. the pool/grounds might be disappointing if you want an elaborately themed swimming area and walkways.
Transportation:
The Poly has boat or monorail transportation to the MK. It is in the unique position to also have direct monorail transportation to Epcot. You can walk from the Poly to the TTC to take the Epcot monorail line (no changes). All other theme parks are accessible by bus transportation.
The CR has the option to walk to/from the MK and the monorail to the MK. The CR is the ONLY resort that allows you to walk to the MK. This is a huge advantage when transportation is crowded, especially at times such as the end of the day following parades or fireworks. It is also great for times when the monorail is not working or is on a reduced schedule. Epcot is accessible via monorail, but requires a ride to the TTC on the MK monorail line and then changing at the TTC to the Epcot monorail line. The big advantage of the CR with its walkway to the MK is also that the walkway to the MK passes by the main resort bus stop to the MK. That means that if you are staying at the CR you can easily walk to the MK bus stop and board any resort bus directly. It is very easy, therefore to get to any other resort from the CR. Other monorail resorts are just a monorail ride away and Fort Wilderness and the Wilderness Lodge have a boat from the CR. In short, the CR is the only resort that has direct transportation to every other Disney resort. Awesome if you want to dine at or visit some of the other resorts on property.
Ultimately, I believe that the Poly would be my first choice, but it is a difficult choice and I do sometimes choose the CR before the Poly. It depends upon the individual trip and what I am looking for at the tim.
For most people, going on their first trip to WDW, I recommend the Poly as first choice and the CR as second. (out of your choices)
( Disclaimer: That might change if we knew a little more of the details of how many people are in your party, ages and if you prefer to spend more time in the Epcot or MK areas.)
Good luck!