This is the time when you will always be asking yourself “ Where's the camera”. There will be first that you will know are going to happen ...and firsts that are surprises. So having 2 cameras would be helpful. One for special events that you can plan for, birthdays, first cake, first spaghetti... a D-SLR would be good for this. It gives you more control and sharper images. And takes faster photos.
Other events that occur as surprises, these might happen when you are out and about. At the mall..or park...taking a walk. You may not want to carry a lager camera and accessories with you. A Compact Camera is handy to have at ALL times to capture those little “life moments”.
There is also many small, and compact video cameras that record to memory media that are great to carry with you.
Always took for a camera/camcorder with the highest Optical Zoom. That way you can take photos/video of your little one from a distance. Once a child is old enough to move around independently and see you are close and have something in your hand they want to come see what it is. With a good, long zoom you can stay out of their area of interest and get those candid type shots.
Good compacts to look for are around the $199-250 range. Keep in the 10 MP (Megapixel) area.
There are many really good entry level D-SLR Cameras in the $499.
Memory based camcorders and DvD/Memory Hybrids can be found in the $250 + price range.
The Hybrids are nice. You can record on either memory and edit on your computer or burn directly to DvD and make copies for relatives.