"any case fan" is a very general statement. Case fans come in a variety of sizes. The most common sizes are 60mm, 80mm, 120mm, and 140mm diameters. They also come in a variety of fan speeds. Some fans are variable speed fans which can be controlled several ways.
You'll have to measure the diamer of the fan you want to replace. If you need to convert inches to mm just go to Google. For example if you measured a diameter of 3.75 inches just type in: 3.75 inches in mm. The answer will appear immediately.
It would also help if you could identify the speed (rpm) of the fan you want to replace. That isn't always easy. There may or may not be an information label on the fan. Northgate like Dell, HP, and other off the shelf pc's do not include detailed information about components.
I see you already know you fan has a small 3 pin connector.
As jsc already mentioned, once you know the diameter of the fan you can go to an online vendor's web site to select an appropriate fan.
If you are interested in a case fan that is relatively quiet, then here is a link to a web site with useful information about quiet fans and a recommended list of fans:
http://www.silentpcreview.com/article63-page2.html