The first suggestion is that when you download them to your computer you place the pictures in folders by name of what they were of. For instance if you took pictures at the state convention this summer you may want to put them in a folder called Kiwanis Georgia Convention August 2005. Then when you want to see a picture from the convention it will be easy to find. I group on my computer by either the event or in the case of generic pictures in a folder by month and year. You may also want to either put these folders in My Pictures or some other folder that you can spot easily and then look within. I have a folder I call Pictures that I have all my pictures in.
Make sure you also backup your pictures to external media such as a CD. I copy mine to a CD with each CD containing one or more events (folders on your hard drive) so still easy to find. Then if your hard drive crashes or you catch a virus such as ILOVEYOU that wiped out JPG files, you have not lost your pictures. When I was in China I downloaded my pictures on my computer each night and burned a CD of that day's pictures. That way they were on hard drive and computer and more likely to make it back to states.
You will have the option on most cameras of the quality of the picture and sometimes format. If you ever plan on printing the pictures or enlargements I would suggest you shoot in the largest or best quality/resolution. The opposite side of this is that you will not get as many pictures on your storage in the camera as the pictures will take more room. You sometimes have the option to shoot in JPG (almost always available) and Raw (sometimes available) mode. If you shoot in JPG format you will be able to immediately view the pictures on your computer and exchange with friends. If you shoot in Raw format you will again lose space on your media, but will get better quality pictures, however you will have to edit and save each in JPG format on your computer before viewing with normal programs such as browsers. So for the average person I would suggest JPG format in highest resolution.
There are a number of editing programs you can use that are available. My current favorite is Adobe Photoshop Elements. This is relatively inexpensive at about $99. The program will allow you to edit the pictures in a number of ways and improve your pictures. If you shoot in RAX format you can actually modify exposure and other settings. I shoot in RAX mode and was surprised on returning form my recent trip to China and looking at my pictures that I was actually able to see stuff in dark rooms my naked eye did not see.
I will be conducting a session on web pages and another session on digital photos at the Fall Training conference.