E., I guess it depends on what you want. I used to have a Sony CyberShot. It was small and took great pictures and great video, but it broke after one year (weeks after the warranty ran out). I had to pay $150 to have it repaired and it worked for less than a year and again stopped working. I only paid $300 for it, so I decided not to have it fixed again.
Now, I have a Cannon PowerShot S3 IS. It is amazing, it takes great pictures and video, but it is bigger and it cost about $500. I am a biologist, so I take it out in the field with me and have taken some amazing wildlife shots with it.....but 99% of our pictures are of the kids. I like that it does not have a pause between when you press the button and when it actually takes the picture (that is common in less expensive cameras) so we don't miss any of the action shots with the kids. This will probably be more important once they get older and start playing sports.
OK, megapixles, more is better. Basically it is how many dots per square inch make up the picture. So more dots = better detail, less dots = blurry or grainy.
Most cameras come with a memory card that is too small for "real" use, especially if the camera also takes video. So, you usually end up buying another card that is bigger, and they are expensive. You can look online and figure out how many pictures they will hold. I have a 1 gig card and have not filled it up (but I download frequently).
As for a printer, I have an old printer (about 7 years old) and it does a nice job of printing pictures, especially if I use photopaper (can buy it almost anywhere). So, I wouldn't get an expensive printer.
Lastly, one thing that we really like about our Cannon is that it uses AA batteries. I bought rechargable AAs, and always have an extra set in the bag. With our old camera, the battery would always die just when you needed the camera, and we'd have to wait until it was plugged in for a few hours to charge before we could use it again.
I hope this helps, feel free to contact me if you have more questions.