What is the best digital camera that I can buy to start using for photography?  

I have the Kodak Easy Share and it is great. Pictures come out crisp and are easy to print on the docking station or download to your computer. There are several versions of this camera. The higher the pixel count the better the resolution.

It depends on what you want to do with the camera. For a family camera a compact Canon, Nikon, or Kodak would be a good choice. If you are serious and want a camera that will grow with you as your skills improve you may want to look at an entry level Canon or Nikon DSLR.

That depends on a lot of things, budget, interest, do you want it for something else too etc.

There's lot of good cameras if you want a point and shoot camera. If you want something with a bit more option but don't want to go for a DSLR at once, there's cameras like the Canon powershoot. You can't change lenses but there's more options than for the small compacts. You can get special close-up and tele extensions for the lens. If you want even more options, then the starter DSLRs are getting really good.

As for which brand, my advice would be to go to a photoshop and check if they let you try a few. Or maybe you have friends with different brand cameras? There's something good and something bad with most brands, so which one's the best for you is more a matter of taste than how good the different cameras are.

As for taking picutres of babies, you might want to check for a camera which is good at taking pictures in low light. Then you can get some shots of them inside without having to use a flash all the time.

While your babies are little, most cameras on the market will cope. As they start to get more active, you will need something that is more versatile, with little "shutter lag" (shutter lag is the time lapse between pressing the shutter and the camera actually taking the picture. It is worse in low light and with cameras that have slower focusing systems) and a longer lens. When they start to run and play with others, only a fairly good quality camera is going to give you a high proportion of "keepers".

So, start with a camera you are not going to have to replace every few months: The best "compacts" cameras are without doubt those from Canon and Panasonic. THey work best in room light or dim conditions, have high image quality, and enough extra features to grow with you and your babe.
A camera with more optical zoom is very useful: 3x is the basic offering, but 5x 6x 10x 12x are all available in cameras small enough to carry with you. Again, I suggest Panasonic or Canon, both companies that put image quality ahead of features.

ordinary use for taking picture, no need to spend so much money. You can just buy a compact camera. Any brand will do. Anyway Cannon is my recomment.

Canon and Nikon are the best digital camera to use weather you are a pro od a beginner. canon and nikon wont let you down :)