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Home-based hosting means you have more control over the hosting environment, although you lack the economies of scale of the professional datacenter. You are responsible for all the security and backup implementations. Many web publishers (including myself) would love to be able to host from home, but the reality of the situation makes professional hosting a better choice.
If you decide to go for a hosting package, you should avoid buying your hosting and domain from the same provider. Controlling your domain is paramount, you don't want it in the hands of your hosting company if you ever want to move the site to a new host.
Geographical location is important for ranking as well as performance (ping time). The former can be mitigated via the webmaster interfaces of the search engines (eg. Google Webmaster Tools). You have to balance geographical location against hosting costs, as local hosting can frequently cost more.
What questions to ask? Joomla can be installed on most popular hosting plans, some have "one-click" installation tools, which add convenience at the expense of flexibility. You should probably install it yourself. You should ask questions about their network, service levels, how many sites per server and what CPU limits are imposed (for shared hosting), and you should read every word of their terms of service and ask anything, however basic it may seem, that you don't understand in those terms.