The cheapest Nintendo DS ever obtained would be one given for free, either as a gift or as a prize. The common price of a Nintendo DS is $139.99 however, these have been on sale for as low as $99.99 during specials such as during holiday season.
You could've just searched Nintendo DS Lite. :) Nintendo DS Lite: Thinner Weighs Less Screens = Brighter Buttons = More Comfortably Arranged Noise = Wider Ranger Games = Game Boy Advanced, and Nintendo DS. (ONLY). Price = Same.
There are several types of Nintendo DS systems ranging from the Nintendo DS, Nintendo DS Lite, Nintendo DSi, and Nintendo DSi XL. The newest version of the Nintendo DS is the Nintendo 3DS and Nintendo 3DS XL.
It costs £99.99 In USA it costs around $129. The average cost of the Nintendo DSLite is about $130. If you buy a bundle package; the cost will be higher in price, and will vary! Sometimes you can get the DSlite at promotional temporary price reductions!