Your OS should be installed on an internal HDD. It would be pointless to install the OS on an external drive since it wouldn’t operate correctly, or most likely at all, on any other computer anyway. Also, if this is going to be a gaming rig, your internal HDD should also be where you plan to install your games. Otherwise, you risk losing performance due to the significant difference in BUS speeds between USB and SATA.
If you plan on Installing Windows 7 on it’s own drive, seperate from anything else, you will need at least a 20GB HDD for the 64 bit OS. You could get by with that, but I would recommend you get at least a 30 GB, to ensure that you have ample “virtual memory” available to the OS. Windows systems, regardless of the amount of RAM you have, will still hammer virtual memory.
Also, if you plan on using a brand new 1 TB drive as an external, be sure you get a quality enclosure for it. With the abuse that most external HDD take, you should avoid 3.5" drives for that purpose. 2.5" HDD are built primarily for mobile applications, and can handle more abuse. Get a 2.5" drive to stick in an external enclosure.