External Hard drive

Any external HD can be used.

Needs to be formated

Need the correct connector for your particular Mac

https://support.apple.com/en-us/HT202784

Yes, as leroydouglas says. But if you plan to use it for Time Machine then know that 3x the amount of space of the data you're backing up is recommended. Also, if you are going to use it for TM you don't have to go for a more expensive SSD, as any rotational drive will suffice. That's because after the initial backup, the rest of the incremental backs take little time and you can continue to work while TM is backing up.