iPhone 2G Unlock - Firmware?

[js0873xx]

I'm wanting to jailbreak and unlock an iPhone 2G. I'm currently on IOS 3.0 with baseband 04.05.04_G. Most of the updates I've seen are used going from IOS 3.1.3, the latest SW for the iPhone 2G. Should I first update my software through iTunes to 3.1.3 before going through a jailbreak/unlock process or will that lose my baseband and I really should preserve it? Basically, will the standard baseband Apple provides for the iPhone 2G on IOS 3.1.3 work just fine on a jailbreak/unlock?