Hi and welcome aboard.
You may want to talk to a shop that sells running rigging as there is more to it than just diameter. Different types of line have different strengths and strech ratios. I recently replaced all my 3/8" diameter halyards with 5/16" lines made of Dyneema which has higher ultimate strength and less strech than the old lines. West Marine has a pretty good guide to lines in their catalog that would give you a pretty good place to start.
St Anna is right too, you have to use a diameter that will fit the sheeves too.