Since some time, very cheap WLAN breakout boards with the SoC ESP8266 from China hits the market. Besides the possibility to extend your existing projects with WLAN (WiFi) access (eg. Arduino based ones) you can develop even simple Internet of Things applications without the need of an extra microcontroller.
The Arduino Uno is a development board with the ATMEL ATmega328P chip in a DIP package. It has an USB port, which is provided by an additional ATmega16U.
The Arduino Nano is a small development board, which is particularly well suited for direct development on breadboards. Through the USB connection software updates can be applied quickly and easily.
After a few small projects with the Arduino you may realize that the program memory for the sketches is rather small sized. So it is time to search for something bigger. You should look at the Arduino Mega 2560, which almost brings much more program memory, tons of new ports, more variable memory and additional static EEPROM memory with it. It is worth noting that the board has 4 hardware serial ports, which makes communication between other Arduinos much easier.