I have an unlocked iPhone 2G,which I've been using on Orange UK for 2 years. I want to change to Vodafone (better reception where I live). I think it was probably originally an O2 phone (as they all were in UK at that time), so, if I ''restore factory settings'', will it revert to O2, or will I then be able to use it ''officially'' as a Vodafone iPhone? Do I need carrier settings for this? or will they come when I insert my Vodafone simcard?

If your Iphone is officially unlocked then it should work with any (other) network compatible SIM card - just insert a friend SIM on another network (or just get a 'free' Vodafone pre-paid starter SIM for testing) and turn-on the unit - if it is locked in any way, it will tell you!
When you do a factory reset, your unit will normally reverted to original 'o2' BRANDING and defaults: this can only be removed by reflashing/reprogramming your iPhone with 'generic' Apple Iphone firmware. 'Branding' in general in an unlock hanset will not stop you from using most of the resources of your new network but 'unbranding' (andor 'unlocking') can always be performed by a qualified technician.
Hope it helps: let me know how you go! Have fun.