I mean any updates, upgrades that need to be done to the server should be taken care of by the provider. I don't know much about dedicated servers and maintaining them, so I would prefer to go with a company that can provide those services.
your best bet is to get a server and outsource management, otherwise checkout serverwizards I wont name any names but hired a guy from here 2 weeks ago, I was still waiting on work to be done just 2 days ago. I switched to serverwizards.com and after contracting them my new server was completely set up, software and firewalls installed, ssl configured as well as fantastico setup on the theme of my choice and this is all well I slept. Next morning boom server is complete. They manage my network and will be doing the management for all my dedicated servers
Many server companies have differnet levels/meaning of dedicated. Find some companies that you are interested in, find some reviews on their service, and contact them and ask to see a copy of their contract/sla what have you so you can determine which one will work best for you. Only you know what will work for you.