The primary object of fusing the equipment is to prevent fire. Therefore when you have two transformers it is best to fuse both primaries. You can achieve finer control by fusing the secondaries too.
As a very rough but practical guide, to size you fuse you need to know the maximum current consumption during normal operation and choose one that is (arguably) 1.5x that current. First try a quick blow and move to an anti-surge if it keeps blowing.