What are the differences between the various partition tables?

The options correspond to the various partitioning systems supported in libparted; there's not much documentation, but looking at the source code:

• aix provides support for the volumes used in IBM’s AIX (which introduced what we now know as LVM);
• amiga provides support for the Amiga’s RDB partitioning scheme;
• bsd provides support for BSD disk labels;
• dvh provides support for SGI disk volume headers;
• gpt provides support for GUID partition tables;
• mac provides support for old (pre-GPT) Apple partition tables;
• msdos provides support for DOS-style MBR partition tables;
• pc98 provides support for PC-98 partition tables;
• sun provides support for Sun’s partitioning scheme;
• loop provides support for raw disk access (loopback-style) — I’m not sure about the uses for this one.

As you can see, the majority of these are for older systems, and you probably won’t need to create a partition table of any type other than gpt or msdos.

For a new disk, I recommend gpt: it allows more partitions, it can be booted even in pre-UEFI systems (using grub), and supports disks larger than 2 TiB (up to 8 ZiB for 512-byte sector disks). Actually, if you don’t need to boot from the disk, I’d recommend not using a partitioning scheme at all and simply adding the whole disk to mdadm, LVM, or a zpool, depending on whether you use LVM (on top of mdadm or not) or ZFS.

Yes msdos is the Master Boot Record based partioning.

You should either go with msdos or with gpt. You will have to go with gpt if you want more than 7 partitions (unless you want a non-standard MBR, which I don't recommend, you never know what utilities assume the msdos/windows restrictions). You also have to go with gpt if you have drives > 2Tb.

If this is a Linux only disc that will never go into a really old Linux system not supporting gpt, then going with gpt is the easiest.