This has actually been quite useful. Electrum is pretty much what I was looking for (or paper wallets, which I've learned a little bit about as well). Since the address is generated offline, I don't have to trust anyone other than myself to hold the bitcoin. I know that I have to trust someone when I buy them, but I don't mind that since it's only for a short period of time. I can just buy and then transfer to the address that I control. What I wanted to avoid was a situation where I buy some bit coin, and then someone holds it and I have no way of knowing if they actually bought it, or if they still have it, or if they could walk off with it.
This is the case with Xapo for example. I'm not saying they are risky, I don't know. Based on the interview with their founder that got me thinking about bitcoin, I'm guessing they are okay, but I want to take the risk myself, otherwise, I'm happy just keeping my fiat currency in the bank.
For those who got into things like "technically not encrypted" or "linux distro" you're on the edge of my technical understanding, and if bitcoin is ever going to take off, it'll have to be accessible to people much less technically inclined than I am. I hope that is the direction it goes. If so, it's a good time to get into it.
Thanks for your help all.