You can always go with nodemcu with wifi and storage on board. ~$2.5 on aliexpress with shipping
Personally I've bought from this one: http://www.aliexpress.com/item/NodeMcu-Lua-WIFI-development-...
So far tested 3 units and they work without any problem, packaging was also very good.
I don't see any cheaper than those currently, but once you have everything tested, if you want to cut the cost you can always just use esp8266 directly which goes for $1.8
Furthermore, their processing power is orders of magnitude apart, as is RAM and storage. NodeMCU targets embedded, and there are plenty of cases where a rpi is used but a NodeMCU would be more than sufficient. But that doesn't mean that they're equivalent, there are also plenty of use cases where a NodeMCU is horribly underpowered.