I don't know what your budget is for accommodations. I do know that two full weeks is hard in just a hotel room. For me, even with just the 3 of you, I would think you may want a kitchen or kitchenette, as well as laundry room or facilities close by.
For our first (well, many) few trips, we stayed on Disney property. I liked the most the convenience of not needing to drive. If you are coming from another country, this is especially convenient.
That being said, that does not rule out the Downtown Disney hotels, as they have a great bus system to take you to the Disney parks very easily. They also are walking distance to the Downtown Disney shopping/dining area (and Disneyquest) as well as Crossroads shopping center, which has many mid-price restaurants and some liquor/grocery store (Gooding's which I do not like really anymore, as they're super overpriced and don't carry a good selection).
You can also look into the Swan and Dolphin, which are, in my opinion, in the best location on Disney property. You can walk right next door to the Boardwalk and Epcot and Disney Hollywood Studios. You can take the boat launch to Epcot and DHS. They have a wonderful pool (that you may or may not use in February). But, it is a hotel room.
You can also look into renting Disney Vacation Club points, and get a one bedroom villa at the Boardwalk Villas or the Beach Club Villas. Do some research, and you may find them appealing. A full kitchen (and you can order groceries from Garden Grocer) and a washer/dryer in the room. Yeah!
We have outgrown staying on property, as we've been so many times that we'd rather have the space of a Marriott Condo nearby and drive. We like a lot of space, and only spend maybe half days at the parks now. I'd love to share any info I can with you - just PM me!