Securely allow scripts to create files

[badkneecap]

I'm in the process of rebuiling a server for the third time now because it's been compromised. My biggest fear is that I'm configuring Plesk to allow functionality that opens security holes that essentially allows hackers to get in.

I have several sites that upload .jpg images. I have software on the server that takes the uploaded image and resizes it and saves it under a new name. What is the proper way to allow visitors to do this without compromising the security?