A.,
The most basic stuff you need is an album; acid free paper, glue and pens; scissors; and your favorite pics. And a little imagination goes a long way...
As far as albums go, it depends on what you want to do. Do you want to make a album for each child and keep adding pics to it? Do you want to send copies of the pages you make to the grandparents so they can watch the kids grow up too? If you do, you may want to go with an album that has 8.5x11 in paper - it will make it easier to color copy the pages (Just make sure you tell the people at the copy store that you took all the pics yourself - they have issues with copying photos that the studios take.)
I'm not fancy with the scrapbooking. I don't use all the little embelishments and "pop-up" things that some people use. They can get really expensive for just one piece.
The cost of each piece of paper can be a deal or it can steal money away from your wallet.
By the time you're done with your page you can spend anywhere from two to ten dollars a page.
I use basic colors for paper, most of the time. (I get more paper that way when I buy it) Then I make my own borders and draw things on paper or make cut outs to go with the theme of the photos. I use very few stickers. My "pop-up"s end up being the things I've kept like name tags, locks of hair, and other things I didn't feel like throwing away because of the memory it invoked.
I hope this helps.
HP