Ext2 does not do journalling. I.e. if have a power-loss or something like that, there is a probability to lose file meta-data with ext2. Plus, a fsck-run is absolutely needed after a crash which will take large amounts of time on current sized disks.
Thus, just use ext3 of xfs, which do both have journaling. mkfs.xfs runs faster. ext4 is relatively new, and one is usually a little conservative when it comes to filesystems.
If you want to use your complete disk under linux, you do not even need to partition it. You can just use /dev/sdX then when creating or mounting the disk.
If you want to partition it, use cfdisk, since it has a convenient user interface.
Be sure to use the right devices for creating the filesystem. Check via
What devices are available and already in use.
hdparm -i /dev/sdX
shows the vendor/model information and size and more to double check, if you get the right device.
Create filesystem then:
Test to mount it via
mount /dev/sdX /mnt/point
If the mount point does not exist, you have to create it first via mkdir.
You can change the ownership of the base directory after mounting it via
chown user:group /mnt/point
To mount the disk after each boot, usually you configure it via /etc/fstab
/dev/sdX /mnt/point auto auto,defaults 0 0
Since you use a Live-CD, perhaps they have a different style of configuration.
To check if some hardware problems happened during mkfs you can enter
and check the most recent output.
On alternative to having to specify a device name in fstab is to specify a label during filesystem creation (e.g. mkfs.ext3 -L name) and use LABEL=name in the fstab (or with mount) instead of the device name.