I talked with an apple support person today. She advised me to purchase an external hard drive to back up my files before she helps me update my computer. I need to know exactly what it is that I need to purchase. Thanks you

I recommend drives from OWC (MacSales.com) as they have proven reliability, excellent customer support and warranties.  Consider one of these that's 2 ½ - 3 times the size of the drive you're backing up: OWC Mercury Elite Pro . It's self powered which takes the load off of there iMac's ports.

I happen to like these Elite Pro Minis -

https://eshop.macsales.com/item/OWC/MEPMTCP10/#includes

This is a recommended Mac-centric vendor and the customer support is great. (I have no connection to them except being a repeat customer).

Best thing to do with any external drive: plug it in and then erase it - whatever is on it, you do not need, Then launch Time Machine, choose the new external, and it'll do the rest.

As stated, larger than what you have at least 3 times. More is better. Especially for Time Machine.

If you don't care about long term, cheap works. But you get what you pay for and if it is cheap. It will likely fail soon.

Follow these instructions to backup your computer using Time Machine:

Back up your Mac with Time Machine - Apple Support

Any Mac external drive will work.