A USPS flat rate padded envelope would probably be the cheapest. $5.95 last time I checked to ship with that. Which, I think, is actually the 'lowest' USPS will ship anyway as I think that's the bottom end of their 'regular' shipping scale (under 1lb and within the same zone- whereas the flat rate is regardless of weight and to anywhere within the US as long as it fits in the package). A small flat rate box is actually cheaper; around $5.80- but you'd need some sort of 'protection' around the product, bubble wrap or something (the padded envelope you ought to be able to just shove it in there and slap a label on it!)
I always double check with calculators with UPS and Fedex, but usually, for smaller items- flat rate is the way to go. Especially if it's small but heavy (like tools or something made of solid metal); because flat rate pricing doesn't change with weight.