This is more of a business question then anything else. It really depends on your customer and how much you would be responsible for their web stie after the initial release. My advice would be to have the customer setup their own hosting account and supply you with access to it. What I normally do for customers who do not understand the process I will get everything setup in their name. This just with keep everything separate for business reasons.

Plus if anything were to every happen with your own web site it will affect this customer site also and that could lead to problems with them