I am interested in the following: I want to have on server(DS/VDS) an OS which I can access with some kind of remote desktop. So this is kinda virtual machine but not on my drive, but in the internet.
What should I look for?
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I would guess any server like this can be set up for RDP if you have access to configure it as you want - A VPS or DS would suffice (although no restrictions really on DS other than maybe some firewall issues but this is so server/company dependent). I would suggest you speak to a datacenter and see what you can get (or phone a web hosting company).