Nope, you need to buy an HDMI cable seperate. Fortunately, ANY HDMI cable will work. It's just how much you want to pay for it that matters.
Just make sure your TV supports HDMI and you're good to go. As for audio, if you have a surround receiver, you can plug optical or the AV cables in. Just ask here if you encounter any problems when setting up.
I got the dualshock3, but I haven't really found it worth it. However, my opinion might change if MGS4 does it extremely well.