Do you think such a dedicated programmed server of average quality would cost more to rent than an average php server?
Definately. But only because an average php server is dirt cheap, and you have to share it with others. In Denmark a decent dedicated server with a proper service plan will set you back about 50-75 USD a month. You can get it cheaper if you want (you could even do it yourself if you really wanted too) but it's probably not worth the extra work.