If the phone is unlocked, you can use any SIM in it, but you'll need to set up things like the data conenction yourself. If you put the SIM in, you may get a text saying "It looks as though something's changed" and promising to send you a configuration file. If this doesn't happen, text the word WEB to 40127 and the details should come back. If nothing seems to appear, go into Messages, then hit Menu and look for Configuration messages and the details should be there. Tap on that and it'll install the correct APN.
SMS should set itself up from the SIM, but you can also make sure there's an entry in Message Centre Number under the same menu. The same should happen for voicemail settings (message centre number should pick up automatically).
If any of this doesn't happen, come back here as there are people who can talk you through the processes. If your daughter is going to be using her mobile for all internet access, it'll be worth considering whether to put some additional data temporarily on her contract. There are bundles available which can be added and removed at will, rather than upgrading the whole contract.
Also, if her contract has been fulfilled (ie gone past the original minimum term), it would be worth going SIM only. I always recommend the 30-day rolling option in this case. It's a little more expensive, but you can upgrade at any time if you have a hardware problem, rather then being locked in for 12 months. But then again, you'll have a new handset with its own warranty.
One final thought: if you can get the phone PAYG from Vodafone, you can still put a contract SIM in it. It may be cheaper that way, it'll be set up for Vodafone (albeit locked to the network) and the shop should be able to help you with setup.
