I already have a hosting service that I'm pretty satisfied + I'd like to keep file structure on the server as it is now (there's separate folder for cloud service, dropbox alternative, e-mail etc.) + I don't want to redirect my current domain anywhere else (and I don't really need another domain) BUT option do build stores without solutions such as Magento sounds really tempting.

I guess that I can download files from your server and reupload them on mine, but that's going to be a hassle.