I'm using Ubuntu Linux on my computer to type this, and I've been a regular Linux user for the better part of the last 5 years.
I have to be honest, if by "making DVDs" you mean video editing, you're going to be disappointed with what any version of Linux has to offer. The tools Linux has for the average home user's video editing needs are far, far behind what Microsoft and Apple give away for free with their systems.
That aside, Linux has excellent tools for the other needs you mentioned, and any major Linux version you try is going to have all the major tools available. The key differences between Linux versions (commonly called "distros" or "distributions") are generally found in default installed software, how you obtain new software (package management), and maybe hardware detection.
Personally, I would recommend Ubuntu. There are other excellent choices out there (Fedora, SUSE), but I give Ubuntu the nod for its excellent combination of default software, hardware support, and tools for installing new software. Plus, it has a great community that will help you get started.
[ADDITIONAL INFO REGARDING VIDEO EDITING -
I'm referring to software accessible to the average home user. I am NOT referring to professional, Hollywood-level software. There is nothing available on Linux that compares to Apple's iMovie or Microsoft's Windows Movie Maker, which is what I assume the asker is hoping for. If you know of such a program, I'd be happy to hear about it.]