You can host from your own computer quite easily. Of course this will depend on the quality of your internet connection.
If you are doing it regularly or persistently it will be worth getting a dedicated machine. Depending on the complexity of the projects a Mac mini (plain or server model) might well do the trick.
The problem with remote hosting for BIMserver is that the application has to be running so you have to use a dedicated server. Last I checked this starts at about $200US/month.