Website setup assisatance needed please

I am working with an easy to configure WordPress theme that came with training designed for restaurants so I believe it will be fairly easy to put together. I just needed help with the logistics. I am new to IM/OM and have never built a WordPress website and need some advice from someone who has done something similar to what I am doing. I am building a site for a restuarant that already has an established website/business but their website needs a totally new re-work. I am not sure the right way to approach this from the prospective of building the site since their hosting (Godaddy which I am unclear as to why the people here seem to dislike their hosting?) has only 1 domain host setup so I am unsure how to build the environment and where the is the best place to build it before ultimately rolling the site out as their new main site in hopes to retain all the Google juice they have held for a while now along with the good reviews they have built up. I definitely do not want to lose that for my client. Please consider the above as well as let me know if it is a good strategy to setup the WordPress install under my hosting and domain name for now only to switch it to their hosting/settings as I believe the client is stuck on their hosting. I need the best strategy here. Anybody with experience in this matter advice is welcomed and highly appreciated. THANKS A LOT!