If you need to change the API, then hosting can become more expensive, as only higher tiers of hosting product usually allow you to deploy custom changes to the back end.
If however you are just wanting to change the look and feel and tweak the UI, leveraging the existing API set, a lot of hosts will allow you to deploy your own Theme Components at no extra cost (depending on the host and product level you are on!).
You will need to discuss this with a potential host.
All that said, if your “module” is novel and sophisticated enough it will require significant knowledge to write and so the hosting part will probably be really easy if you are that experienced. Developing Plugins is non-trivial and there is a bit of a learning curve. I’d argue a much steeper curve than the relatively easy path to deploy your own default instance on your own VPS (thanks in large part to CDCK’s effort to make things straightforward).