The Raspberry Pi minimally needs a micro USB-B cord to power it. If you have a phone charger, aside from an iPhone, it will likely use this cable since the EU made it mandatory for smartphones. So, you probably don't even need to buy another wall adapter or cable if you look around. You can also plug it into a computer to power it, though you are not able to communicate with the computer over it. Additionally, an Ethernet cable connecting it to the same LAN as a computer is one of the easiest ways to get started. Unless you can figure out what IP address the Raspberry Pi will get, you will also need a keyboard and a monitor or tv capable of using either HDMI or the yellow RCA connector.
The Raspberry Pi does not come with an SD card, which you will also need. You will need to install an operating system on it as well, so it should be at least 4GB to be comfortable. Some SD cards are faster than others. Higher speed is denoted by a higher "class" number. This class will primarily effect install, startup, and upgrade times and there is no mandatory minimum.