The iphone 3g is too under powered to run construct games well one, don't bother. even the 4 is kinda wimpy. the 4S is probably the lowest id go for, iphone wise.
Android wise you can get a virgin mobile optimus slider for example for about $30-$40, and you can still use it without activating it on the virgin mobile network, so no monthly fee etc.
works great as a cheap mp3 player/youtube/movie player as well.
But if you can swing it, go for a second hand google nexus 7 tablet. they are about $150 second hand.