For a Headless Raspberry Pi Setup, you will need a Raspberry Pi Model B. The reason you need a Model B is that it has an Ethernet port.
You will need a SD card with Raspbian on it, the general recommendation is a Class 4 with 4GB or more of space.
You will also need a Ethernet cable to plug into a router for the initial setup. If you have a WiFi adapter that the Raspberry Pi is able to power, you will still need an Ethernet cable for the initial setup.
A main concern is that you will need a Micro USB power supply. Most phone chargers do the job, but if you notice bizarre behaviour from your Pi, you may need a different phone charger.