Creating my own domain & website

You will need to register the domain name of the church at a domain registrar. I usually recommend http://www.namecheap.com.
Depending on the domain extension (.com, .net, .org, etc), the price of the domain varies. For .com domains, it's usually 10$ a pop. Note that this is usually a yearly fee, and the moment you stop paying, the domain is no longer registered to your name.

Then you will need a webhosting service to actually host the church website in. This is where you will put all your code, databases, files, and so on. Personally, I have used http://www.arvixe.com. It's around 56$ every 6 months for a standard PHP hosting plan, if my memory serves me right. The website we were planning on having with Nagare had a nice host too, but I forgot what the host was... Note that Arvixe offers a "Free for a lifetime" domain registration, but there's a tiny gotcha: You will own the domain for as long as you are with Arvixe: The moment you stop paying for their hosting services you will lose both their hosting AND the domain.

quote Vermillion

Note that Arvixe offers a "Free for a lifetime" domain registration, but there's a tiny gotcha: You will own the domain for as long as you are with Arvixe: The moment you stop paying for their hosting services you will lose both their hosting AND the domain.

As far as I can tell that's not true, as it says here you can unlock the domain from the billing page.

Ahh I see your point, it's not like they steal the domain off you when you leave though, you're free to transfer it somewhere else

It's still your domain, you just have to start paying for it.