For a compact, you'd be best off with 4mm sheet, which is about 5/16 of an inch.
Then reinforce the upper part of the bucket with a 2x4 inch tube, weld on a grader style bucket blade, some 3/8" flatbar from the bucket lip to aforementioned tube, and a 1/4" strip under the rear edge of the bucket as wear protection. Also weld 3 or 4 lengths of this 1/4" flatbar underneath lengthwise. Also weld some of this 1/4" plate where you'd weld on the quick attach hooks.
My 6 1/2 foot wide loader bucket came off a small Atlas wheel loader, i think a 6 ton model, and its about constructed that way. Using 3/8" sheets is a waste of money, and more important, lift capacity.