My first issue.

Ok, I haven't had my iMac for a week yet & though I am learning how to use it I know this is a problem I don't like. Sometimes when I try to start a program it just runs the little icon/curser colorful spin and never stops. This begun after some sort of update & I started the computer over.

Also when it gets stuck like this what can I do? I see the control alt delete doesn't work & I would hate to keep having to yank the power.

Use Cmd+Alt+Esc (Apple+Option+Escape)

You will see a list of running applications... the app in question will have a "(not responding)" next to it... Highlight it, then click Force Quit.

More importantly... what app are you having this problem with?

Another thing that will bring happiness to you, is buy another 1x2GB of RAM and get it into your machine. The beachball will go away for most of your needs. Best money spend since you bought your machine.