Also if I use there free blog does that severly limit what I can and can not do? Like using the custom templates, feedburners, and linking to other sites that I really like?
Others already answered most of your questions. Let me address this, and I'll make one additional point.
(I should emphasize that with a self-hosted install, you ONLY pay for your domain name, <$10 year, and your web space, which is $100 - $120/year tops; WordPress is free.)
Wordpress.com (free WP) allows you to add widgets just as a self-hosted installation does.Therefore, you can certainly use FeedBurner, and you should, because if and when you move to self-hosted, YOU are the only person who has to do anything to get your new site on the same feed--and that is exceedingly simple to do.
Custom templates have been discussed; to reiterate, on Wordpress.com, you're somewhat limited, but there is still a large variety. You just can't modify them much (which is generally not an issue).
As for linking and the like, not a problem at all. Take a look at the various WP bloggers here: Many are self-hosted, but many are on Wordpress.com as well. At first glance, it's quite difficult to tell them apart, other than the URL.
Now, the additional point I wanted to make: From your initial post, it sounded like you have the wherewithal and commitment to self-host your own blog. If you're sure that's what you want to do, then by all means, dive right in. As Matticus said, it's not difficult (trust me on this!!
), and any number of us would be willing to take you step-by-step.
Good luck, and hope to see your blog soon!