Speed and performance of the website are important in fixing the site’s ranking on search engines. As configurations of the server affects both of those things, the customer should take a close interest in what is being provided and not simply accept the first offer.
RAM and Storage
It is not possible to lay down hard and fast rules about how much RAM and how much disk storage any particular site needs without knowing exactly what the site is. The most important thing is probably to begin with something that sounds reasonable – say, 1 GB of RAM and 20 GB of storage – but make sure that larger configurations, if necessary, can be provided and will not cost an arm and a leg.
There will almost certainly be limits of some sort; find out what they are and what happens if you go beyond them.
Find out what sort of backup is in place and how your data and the site layout itself are protected.
Ask how many IP addresses come with the service. If it doesn’t sound like enough, check the price for adding more.
Unless your server is going to be running games, CPU power is probably not an issue – but check what your allocation is.
Once all of this is in place, monitoring speed and performance becomes very important, especially at the beginning. Check what metrics are available as standard and what can be added – but check also how much assistance the server’s staff will give in configuring metrics and how skilled at that they are. Google Analytics, for example, is capable of providing enormous amounts of extremely useful information but it is simply not as easy to configure as the documentation suggests. Unless the customer’s IT staff have the skills required, outside help may be needed – and that can be expensive.