Ajurina, I would highly recommend the 17 inch iMac if you are going to make a leap into the Mac world for doing video editing.
The Mac mini MIGHT get you by working with non-intensive video editing but bear in mind, this is a SERIOUSLY entry level computer and the graphics card and processor in this thing will be weak. If you enjoy what you do and take it further, your efforts will be hobbled.
The new iMac has the 1.83 GHz Intel Core Duo and Apple has promised that its applications will all be running Universal Binary code if not now, then shortly. Bear in mind, the Mac Mini has a G4 not a G5 and the step up to the iMac will give you performance that is several times faster.
Plus, when you consider everything that the iMac comes with that the Mini doesn't, the price difference is no longer so big. The mini has no monitor or even keyboard and mouse. If you start working with video, you will likely want to be able to burn DVDs and the iMac comes with a Superdrive burner, the mini can only READ DVDs.
Anyhow, if you were just getting a Mac to surf the web or do e-mail or write or something, heck yeah, the Mini is a great product. But if you are planning on working with video, don't even THINK about going with anything less than an iMac. You can do payment plans through Apple if you don't have quite enough cash up front to make the leap. It's just the performance difference for what ends up being a few hundred more dollars more makes the iMac a no-brainer.