Currently I am using a triangle list to render the terrain.

Almost all the tutorials I am reading teach a method of loading the terrain so you can use quads.

Do I want to use quads??

Next.
People keep telling me to run through each row Like right to left and then the next column left to right.
Why and is this how it has to be done? What for?

All I do for storing the vertices is run y 0 to mapsize and x 0 to mapsize.