In order to "see" details, digital cameras need light, just as your eyes do; you'll want one with at least five megapixels. Higher-resolution sensors maintain image quality when you crop and enlarge. Look for a lens with at least a 3x optical zoom for sharp close-ups. Longer-zoom cameras need optical image stabilization to eliminate blurriness. To take pictures one after another, you'll want a brief shot-to-shot time. With the flash on, test the camera at the store. Consider a full-feature camera so you can begin with automatic settings and progress to manual ones; some address red-eye and exposure problems.
For archival-quality prints at home, buy a printer classified as a "photo printer" with at least four inks: cyan, magenta, yellow, and black. Good ones have additional shades to enhance color reproduction. For best quality, look for ink-jets with an ink-drop size as small as possible (about 1 picoliter, or 1 trillionth of a liter). Most printers use dye-based inks, but pigment inks often last longer. Match manufacturer-approved inks with archival paper for images that will last a hundred years or more.