How to run a Django Project on a Personal Run Server
Yes, you will need a static IP address.
If this is your first experiment, my advice would be:
1) Use an old, dedicated PC with no other stuff on it.  Unless you do it just right, you should presume hackers could get anything on the disk...
2) Why make life complex with layer after layer of software?  Install Ubuntu and run a standard server under a Unix OS
3) Be very careful about the rest of your attached network.  Even if the PC is dedicated, unless you properly managed port forwarding, etc., ALL of your computers could be susceptible to attack.
An old friend of mine discovered, back in the Napster peer-to-peer days, that he could basically go and read EVERYTHING on the hard drives of most people who had set up Napster on their computer.
I've been wanting to run my own server for a while and I figured that running one for my django website would be a good start. What do you recommend I use for this? I've been trying to use a Ubuntu Virtual Machine to run it on one of my old laptops that I don't really use anymore until I can buy a dedicated server. 
Should I run it from a Virtual Machine? If so, would Ubuntu be best? That appears to be the case, but I want to be sure before I invest in anything. I want to be able to access the website from other computers, just like any other website. Am I going about this wrong? If so, what can you suggest me?