One option would be simply start out by booting a Linux Live DVD, such as the Ubuntu installation DVD. That way you can try Ubuntu without installing anything onto your computer. The downside is that everything you do on Ubuntu will be gone when you power down the computer. The upside is that you can verify that Ubuntu indeed works, especially that Ubuntu recognizes your graphics card.

Another option would be to purchase a Raspberry Pi. This is a great way of getting to know a little bit about linux, although it's not necessarily quite the same as running say Ubuntu on your desktop computer.