rogerClark:
I'm not using this myself, but I'd recommend you take a look at the lua firmware, it can operate as a basic web server and you can still communicate to the Arduino via Serial , but you'd need to write your own command parser in lua
The word I assume you're looking for is "NodeMCU" (link to firmware) and yeah I really recommend it as well. I wouldn't say it's required to spend a lot of learning time with lua though; in my case I just set it to act as a Wifi-to-serial bridge using some example programs I grabbed from the esp8266.com forums. I don't need an additional speck of lua code in my Arduino sketch after that initial setup.