Connecting ARM cortex m4 to the internet
Various companies (including TI, Murata and Microchip) offer ready-to-go Wifi modules that can interface with a microcontroller via SPI or UART.  Search for CC3000, SN8200, RN171 respectively.  If you're prepared to go further down into the protocol stack murk, they're mostly using Wifi chipsets with SDIO interfaces.  If you're after throughput, the Murata SN820x is nice, but be prepared to write your own SPI stack.  The TI CC3000 is substantially slower (TI claim about 3Mbps of TCP throughput), but iirc they have a free stack that should integrate easily with a TI M4.