Typepad is a hosted service. You can't download it and install it here. That being said, there's really not much difference between the two. WordPress is a very powerful setup, yet is very easy to manage. I really like WordPress. Since it's a One-Click installation (use Advanced Mode so you can add and modify your own themes), it's a snap to set up here.
And, as Independent said, your site here is your own, so you can advertise to your heart's content.
So give it a shot. If you have any problems, ask for help in the Troubleshooting forum. You'll get a quick response.