If more than one person will be using the same camera, buy a separate memory card for each person; this way, everyone can keep their photos separate, and you don't run the risk of deleting someone else's pictures.
If you plan to take a lot of video, it would be a good idea to use a memory card with a good amount of memory (at least 2GB) with a high write speed. While most digital cameras do an average job of capturing video, I would suggest getting a camcorder if video is a priority to you.
When photographing pets, I would suggest using as much natural light as possible. To avoid red/green eye reflection, I would suggest not using a flash or at least using an off camera lighting source. Get down to the pet's level when capturing your image (would you get onto a ladder to take a portrait of a person?).
The best natural light is the light right after sunrise and right before sunset. This light typically lasts for about an hour and is referred to as "Magic hour". It's when the majority of professional natural light photographs are taken, and you will be very surprised how much better your images look when taken during it. Hint: When photographing sunsets, don't use a flash and mount your camera to a tripod.
When shooting objects through glass, don't use a flash and use a polarizing lens filter if your camera is a DSLR. I would also suggest switching your camera to manual focus (if your camera has this option) since the autofocus system of your camera could easily be fooled into focusing on the glass (especially if the glass is dirty) and not your subject.
Most printers allow you to change its setup depending on what type of output you are going to be printing and what type of quality you want. I would suggest setting your printer to "Photo Paper" and its best quality setting before printing your photos. It might take longer to print, but the wait is most definitely worth it.
Lastly, I would make sure that the paper you are using is archival if you want your images to last a lifetime. I would also suggest always handling your prints by their edges, as the oils from a person's fingers can cause your images to fade and discolor over time. If your prints are intended to be framed or put in an album, I'd suggest getting a few pairs of white cotton gloves which can be purchased at most art stores.