http://quiltville.com/scrapusersystem.shtml
Here Bonnie talks about the usefulness of certain sizes.
Also 10 inch squares can easily be cut into 5 inch squares and those can be broken down into 2.5 inch blocks. Like some one else mentioned I would cut the left over 3 inch strip into a 2.5 inch strip. Most likely you will need to any ways because it will not be an accurate 3 inch strip that is left.
Be sure the sizes go together like Bonnie mentioned. When I buy dies for my fabric cutter I look at which ones work together to make certain sized blocks like 12 inch finnished blocks, 12.5 unfinished blocks. I think you need to do the same for how you cut up fabric.
I think sticking with sizes that are used to make 12 inch finnished blocks, like 4.5 in., 3.5 in., 6.5 in., 2.5 in., and or are found as precuts, 5 in., 10 in. and 2.5 inches, will yield cuts that you can use in many patterns that are out there in great numbers.