I need recommendations in purchasing an external hard drive, to back up everything in my computer. What brand and Size?

I have a mid 2010 iMac, version 10.8.2, memory 4GB, 1TB sata disk.
Apple sent me an e-mail last year stating that my imac maybe affected to a recall. They said I have to back up my computer before sending it in to them. So its a great excuse to purchase an external hard drive.
But I am clueless. I would like to know what brand and size of memory is recommened for my imac and my needs. I will be mostly be backing up homevideos and alot of pictures, music, and some documents.
If someone could also explain about time machine? I guess its a whole separte thing from your media. I also would like to keep it affordable. I just purchased an external hard drive from www.macmall.com Seagate Backup Plus 1TB USB 3.0 Portable Drive - Black (STBU1000100).
But I don't know if that was a really great choice because for it to work with time machine I have to reformat certain things, and Im not sure if I would like to have that hassle.
I also wanted to know whats the difference between usb 3.0 and firewire. I read some forums saying that if you are to transfer videos you need to use firewire, and some agreed disagreed. Is that true?
Please help!?
I definitely would like to know what brands of external hard drives are highly recommended and good at price. The one I purchased is it any good?
Thank you!