If you are coding it up yourself I would just host it on any old hardware laying around.
The upgrade path I would use is to grab what ever old gaming pc that the founder already owns. Once everything is up and working, money is coming in, you have customers, then start considering upgrading to an actually dedicated server with redundant power supply and ups. Once that is starting to get old or the company management software has outgrown such setup you have enough data to know what kind of demands you want to apply to a cloud company in terms of reliability, scaling, support and legal.
The upgrade path I would use is to grab what ever old gaming pc that the founder already owns. Once everything is up and working, money is coming in, you have customers, then start considering upgrading to an actually dedicated server with redundant power supply and ups. Once that is starting to get old or the company management software has outgrown such setup you have enough data to know what kind of demands you want to apply to a cloud company in terms of reliability, scaling, support and legal.