Control iTunes remotely on 10.3.9 (or maximum 10.4.11)
I think the trouble you're going to run in to is that much of the remote control software for iTunes out there, especially for the smartphone market, requires an iTunes version that support Digital Audio Control Protocol (DACP, aka "Home Sharing"). Not sure you can get to an iTunes version that supports DACP if your highest OS level is 10.4.11.

For control from another Mac I highly recommend TuneConnect. Very cool little program that lets you remote control iTunes on another Mac from your current Mac. Even streams the cover art and playlist back to the remote app. It uses a daemon approach to controlling iTunes so it works with older, non-home sharing capable, iTunes installations. There's also the simpler iTunes Remote Control which works over Bonjour IIRC -- not quite as fancy, but it gets the job done. Both of those are free.

For control from an iPhone Apple has it's own iTunes Remote you can download from the iOS App Store for free. Works well. Requires home sharing be turned on in iTunes -- so you might be out of luck there if you can't run the latest iTunes on your older iMac.

For an Android device there's TunesRemote (which uses the home sharing protocol, so it requires a newer iTunes installation). TunesRemote is free and open source. There's also Remote for iTunes which also relies on DCAP and costs $5.

For control from a non-Mac machine your best bet is probably still VNC. Just get a remote desktop on the Mac and click away. I couldn't find anything that solves this particular problem. I'll admit I didn't look that hard. :)