Thinking of setting up another portal. We have Portal Alpha in the West so which direction should we do next?

I was thinking of going south. The idea would be to treat our base as the East portal and then create a north and south portal in the nether that are mid way between the east and west portals but in the respective directions. Thoughts?

If someone could loan me a diamond pickaxe that would be awesome. I also heard talk of an obsidian generator if any one wants too make one or point me to the how to video.