Sure; anything you want, as long as it's testing the things you care about!
Again, like in the answer to your previous question, I'd encourage you to go browse the COSI tools at http://cosi-nms.sourceforge.net/ before spending too much time developing in-house stuff.
But on the assumption that you decide to design your tool, here are some more considerations.
Traceroute and ping may or may not be good tools in this regard! Since you care about talking to a web server, why not test the path all the way up the network stack?
For example, you could install lynx, a character-cell web browser, on unix; write a little expect script to hit the web server and fetch a common page (like its index.html); and then run that every 30 minutes.
