What wifi board?

Well I've been playing with an uno for a bit now and want to try my hand in making something that does something useful to me!

I have a camera that can be controlled through wifi with a phone app. I would like to use something like this

HandleNewmowa® DMW-BGGH3 Battery Grip Replacement for Panasonic DMW-BGGH3 and Lumix GH3,Lumix GH4 Digital SLR Camera https://www.amazon.com/dp/B00ME0F0SQ/ref=cm_sw_r_other_apa_eJXXxb0WJRGTX

And add a wifi board so I can controll the camera.

First question is, what is a good board with wifi on it that would be able to handle this?

Second, I'm not sure how to figure out how to figure out the comands to controll the camera. Is there a good way to figure out what the app sends to the camera? The app connects directly to the cameras wifi.

Thank you

The ESP8266 is by far the most popular WiFi development board at the moment.
It has large user base, so many tutorials and great libraries.
And the best part: You can program it using the Arduino IDE, using Ivan Grokhotkov's ESP8266 Arduino Core.
It is a SOC (System On a Chip), which means that you don't need an Arduino to control it, it's a microcontroller on its own. (And a pretty powerful one: 160MHz, 80kB RAM, 1-4MB flash, 9 I/O pins, 1 ADC ..., so many times more powerful than your average Arduino.)

There's quite a lot of topics about it, here on the forum as well.

To figure out the camera's control protocol, you could use a network sniffer app, that intercepts the packets on the network, and displays them (in raw or human readable format). You can then filter by app, or filter by IP-address to see what kind of packets the app sends to the camera, then send those same packets from the PC or ESP8266 to see if it works.
The first one Google Play showed me: Packet Capture.
(If it wasn't a smartphone app, I would use WireShark on my computer to show the packets, but since it's a separate WiFi network, a sniffer app might be easier.)

Ok so I need some more help!

First I got this board Adafruit Feather HUZZAH

OK so I don't know much about all this "http" stuff yet! I did a packet capture and think I see what's going on between the app and the camera. Seems like the camera sends alot of info of the settings available.

Ok so I know that in the attached image, #27 was what the app sent to the camera to change the iso to 640.

I then used my laptop to connect to the cameras wifi. I thought that I should be able to use a browser to send the comand with no luck.

So with all that can someone tell me "what is going on" really just want some links to some helpful info, that will help me learn about this ip stuff.

Thank you guys in advance