Re: ota update help
The jailbreak should work fine. But, you're losing SHSH blog support. That's useful for later returning to 6.1 if necessary.
Honestly, Cydia and the jailbreak community repositories are so slammed right now you're best off restoring via iTunes. The hour it'll take to download and install 6.1 from iTunes will provide you a recent backup, a bit of time for Cydia to catch up, and the SHSH blobs you want going forward.
After that, or skipping that step, simply go to the www.evasi0n.com site and download the appropriate installer version. It's one of the easier jailbreaks. You don't have to bother with holding any keys for set times, etc. Just plug in the device, close iTunes, hit jailbreak, and follow on screen instructions. Those amount to "don't touch your device" and "ok, unlock it and click the new icon." The rest takes care of itself.