If I were you I would first try to build a working server on your own PC. Then when you got something working, and are ready to move onto alpha testing start small and rent a VPS (virtual private server). If you shop around you can usually find one for under $40 per month. Then as your game gets big, you can upgrade as needed.
If node.js isn't working out you could always try to build a PHP, and MySQL server. These have been around for many years now, and Ashley has made Construct 2 very capable of using php, and MySQL as a back-end.