How to upgrade my iPhone 4 to ios 5?

I bought a iphone 4 and the bad thing is that its on ios 4.2.1. Now i wanted to update to 5.1.1 but I'm not able to. I read something about apple not signing there ipsw. I want and need to update so i can download apps cause every time i try to download am app it says it requires ios 5. The only solution i can think of is to update to ios 6, but i'm thinking twice about it cause i hear ios 6 has bugs not only that but as far as I know ios 6 doesn't have an untethered jailbreak and on top of all of that I plan to factory unlock the iphone to use worldwide. Can someone tell me what path to take

See the tutorial and update your mobile my best wishes my friend

Http://iosindex.com/instructions

The latest software update is 6.0.1 there are no bugs in it.

Update iOS Software
Via iTunes:
1) Plug your iPhone into your computer with the Syncing cable
2) Open up iTunes
3) Look on the Devices tab on the left for your iPhone
4) Click on it and under Summary it should show the option to Update it

Via iPhone:
1) Go to Settings
2) Go to General
3) Go to Software Update