Your State of Jailbreak:
Good news! There is a jailbreak available for your iPhone.
redsn0w is a very solid jailbreak that takes just a few minutes to complete and still is about as robust and full featured of a jailbreaking program that you can get. Using redsn0w 0.9.10b1 you get an untethered jailbreak with options including custom bundles and multitasking gestures.