These three options refer to the partition table, which is a small section of the drive reserved to basically describe how the drive will be partitioned.
The Master Boot Record (MBR) is the old way of doing things. It has some limitations like the number of partitions that you can have, how large they can be, etc.
I don't remember what GPT stands for GUID Partition Table and is basically the upgrade and you should be using this unless you have some reason for it. Some old hardware doesn't support it very well, for example.
The third option of no partition will simply make the drive empty, removing whatever partition table already existed. I guess you can do this in an attempt to "clear" the drive if you're going to sell it and you don't want others to read the data in it. This doesn't actually erase the data, so don't rely on this for anything sensitive.
Once you have a partition, you still need to tell the drive how the files inside that partition will be stored. That's what the file system does. In Linux, for example, files have an associated piece of metadata used for things like permissions and ownership, which is different than how Windows does it.
EXT4 is the de-facto standard file system for most Linux distributions today, although there are others you might have heard of like BTRFS, ZFS, and many others.
NTFS is the one used by Windows, which I think replaced FAT32 on Windows around the 2000's. It actually still in use for things like SD Cards and some flash drives, since it's so compatible given it's been around for a long time.
For a flash drive or external drive you can just use NTFS, since it's so popular these days that in all likelihood all operating systems will be able to use it no problem. If you have problems with it, then FAT32.
On the other hand, if you're only going to be plugging this on Linux systems, or you mean to use the drive to install Linux, then choose EXT4.
If you need an example on how you can partition a drive (the details used here might not fit your exact needs, but it might still be helpful):