I imagine dedicated as there is a lot of server load, but some people think that if you have a big board you have to fork out for a dedi server, this is not true. If you find a stable shared hosting provider they will let you host a big board doing this you wouldnt have to worry about RAM/CPU usage etc, but I would contact a shared hosting provider before buying and ask them if you can.
Regarding servers my top would be Softlayer

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