Use the size 10s with a medium weight yarn, thought the 8s might be good too. The size 3 is for thin yarn like sock or baby yarns (though some baby yarns are pretty thick).
Smaller needles will be more sts per inch, so if you want something about 7" wide and you get 6 sts per inch, you need 40 stitches or more. But if you use a larger needle and get 4 sts per inch, you only need 30 sts. Since the bigger needles make larger stitches and rows you don't need as many stitches as you do with the small needles and end up using less yarn for the same measurement. If you use the same number of stitches with the big needles as the smaller ones, you'll use more yarn, but will end up with something a lot larger.
sue- knitting heretic