Whatever you do, make sure the domain name is in YOUR name. You can buy it at http://www.internationalinternetauthority.com/ or any other registrar you feel comfortable with.
If you resign yourself to not knowing and let them buy the domain name you could find down the road that you`re not actually the one deciding who gets what percentage of what, if you know what I mean.
As for the rest of your question, take the advice of the previous posts. There is actually - if my memory serves me right - a podcast on this topic already. I`m 90% sure in one of the SUN podcasts, this is mentioned. Do a search.
Get Your Name in ".com"
at the International Internet Authority