That's just hosting for movable type blogs isn't it? You wouldn't be able to host it unless you had direct access to your files and a database, which I highly doubt they give you.
I dont know what typepad is which doesnt help for staters, but vanilla should run just about anywhere there is a working php&mysql installation (reasonably recent), and you have the ability to upload files and create database tables. If you are missing one of these you could be a bit stumped. But there is a ton of suitable free/cheap hosting out there.
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