Your original post did not in fact state anywhere that you had a MobileMe account.
Also, you seem to be getting a little confused here with terminology which does make a difference.
Rather than a domain, what you in fact have is a domain name that is registered through hostpapa.com - it is not hosted as you say, but registered with them.
Also, iWeb will not and does not 'publish directly to your own domain'. iWeb cannot publish to a domain name or anything - you need a hosting account to be able to publish a website - do you have this? If not, then you will need to purcahse hosting too.
So, if you want to publish your site directly to hostpapa instead of MobileMe, then CNAME is NOT involved in this at all - you DON'T need it. CNAME is only a method of forwarding that you would use to forward your domain name to web.me.com when published on MobileMe. If you do not want to use MobileMe any longer, then you don't need this.
So you say that you have registered a domain name with hostpapa? Do you also have a hosting account with them too if they provide hosting? If not, then you need to purcahse a hosting account from either them or some other company that provides hosting.
When you have your hosting account and assuming that you are using iWeb 09, open iWeb and then click on your site name and your publishing options with become available in the drop down menu - rather than picking publish to MobileMe, select the publish to ftp option instead and fill in your details such as ftp name, username and password and then upload your site after testing your connection.
If you are using iWeb 08, then you'll need to publish to a local folder and use Cyberduck or Yummy ftp etc to upload your site to your server instead.
CNAME is not involved and if you purcahse hosting from another company other than hostpapa, then you will probably have to alter your nameservers so that they point to where your site is now hosted.
If you want to ditch MobileMe, then you don't need to use CNAME at all - it just isn't involved here.