I was thinking of purchasing a domain.
But..
Must I already have a host or can I use a HTML Editor like would www.mydomain.com/index.html be the same as www.geocities.com/my_name/index.hmtl?

many domain name sites will "park" the name until you can find a host to support it. so you can buy your domain name at any time.

the next step is to purchase hosting space that supports a domain name. i think geo has a "plus" package that does this, but you can find a much better package doing a search for a better or same price.

essentially yes, www.mydomain.com/index.html would be the same as www.geocities.com/my_name/index.html after you have the hosting package setup.

once you have your host ready, the host will give you a set of numbers. take those numbers back to the domain name site, plug them into your account, and within a couple days, your domain name will be attached to your website.

I think it would probably be better (cheaper) just to get a hosting package with a free domain, like doteasy (http://www.doteasy.com).. there are others too.

There are also free hosts with free domain hosting, like Netfirms (http://www.netfirms.com) .