Should I use a webhotel or a FREE blog?

Hey

I've found a niche keyword I would like to create a site for so I can (hopefully) get some adsense earnings

So I've been thinking about these two alternatives:
- Buy a webhotel (a place on the ISP server where all my files are hosted together with database). I reckon it costs about $10 pr month.
Here I think of using WordPress software installed on the site (I have to learn how to configure wordpress )

- The other alternative is I register to get a FREE blog from WordPress.com.
Then I register a domain and point this domain to my blog, so the url will not be like:
http://loginname.wordpress.com/
but instead:
http://crazysnowman.com (this domain is just an example)

So I was wondering what I should choose. Of course the free blog looks tempting, but isn't I missing some SEO tweaking possibilites when selecting the free blog compared to full installation? I want the site to become #1 in google (who doesn't want that? ) and get lot of adsense clicks, which alternative should I get?

Here I think of a site with about 10 pages. I also would like to create links between the pages and use rss

It's not suppose to be an either-or choice between paid sites and free sites. You need both esp. when you're creating backlinks.

If you have your own domain, I recommend using WordPress MU (the multi-user version of WordPress at mu.wordpress.org) so you can create hundreds of blogs in your own domain like wordpress.com.