I will attempt to answer your question.
First and foremost, if there's anything on that drive that you want to keep, make sure you copy it to another drive.
Second, if you ever want to plug that drive into a Windows system (a laptop for example) then I would recommend keeping it NTFS. You will still be able to copy files to and from that drive from your linux box. You will not be able to access the drive in Windows once you format at in linux as EXT2/3/JFS/XFS/etc without special drivers.
Now, if you really want to format it. The easiest way to do it is to use GPARTED.
1. Plug the drive in the computer.
2. After Linux Mint has detected and automatically mounted the drive. Right click on it and select Unmount.
3. Open GPARTED... Select /dev/sdb1 (or whatever the drive is -- make sure you select the right one or you will lose all your data).
4. Right click on the partition and select Delete.
5. Right click on the partition and select New.
6. Here you can set the size and type of partition you want.
7. Click Add.
8. Repeat steps 5-7 if you're not creating one huge partition.
9. Click Apply.
For a good discussion on the different types of partitions, start here: http://linuxmint.com/forum/viewtopic.php?f=90&t=13480