You can try rack911.com but I can't remember their pricing. Nothing will be fully automated though. If there is a problem you will want someone like them to log in and poke around… Don't go too low in price to start but month to month you should be able to keep costs down.
I think getting a separate company for support will be better off for you, rather then paying so much more money like that. Platinumservermanagement.com has been a provider I have been using for support, recommend to me as well long time ago and have been very satisfied with the tickets and answers I get every time I have opened a ticket. It's so practical to just open a ticket every time I need their help so I can focus on my clients instead.
You get cPanel managed services from $20 / month to $150 / month ( may be upper limit is a bit more higher with some companies ). The thing is, you get what you pay for and of course some giants charge for their brand name as well. Check around, sort out a list, check reviews and pick the best you think!
In 70 Euro dedicated server with cPanel control is possible but you will receive very basic server and it will cause your web site performance and stability, therefore its always better to increase budget little bit more, so that you will receive the better server as compare to basic ATOM servers
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