Microchip programming with network connectivity
Arduino with a wifi shield or an ethernet shield is a great start. The Arduino IDE is functional, and there are a lot of libraries and great support on here and elsewhere on the web. However the programming language is C++ and typical Arduinos have RAM (1 - 2kB) and clock speed (8 - 16MHz) is on the lower end of things.

OR

Netduino. C# programming language. Better IDE with Microsoft Visual C#, although normal Arduinos can be written for using Visual Studio and the Visual Micro plugin. Much faster clock speed and more RAM, but more power. Arduino shields can be used on the Netduino. The Netduino Plus 2 has ethernet. Some people have had success connecting a WiFly shield for WiFi connectivity.