Hosting - Small multisite project

New to Multisite, but have 15 WP sites under my belt and am looking at a new project that I think Multisite will be ideal for. Client has 7 domains - all inter-related as they come under one parent company (these are not blogs btw but small commercial sites). I thought that if I set up WP with Multisite on one domain then the 6 other domains could be either subdirectories or subdomain with the domain names pointing to them using the Domain plug in. For me this is all theoretical as all I have done is read through the manuals here.
My question is this - as there isn't going to be a lot of content, mainly static pages but with one site having a shop, so the resources needed wouldn't be huge, would I still need to get dedicated hosting? I have a reseller account with Hostgator with plenty of room available, but are there other issues I need to know about?
One bonus question if I may, I plan on trying to use one theme and having different colours (using child themes with edited css?) for each of the different sites, is this easy to set up? I have been using the Genesis framework to this point, but not sure whether their themes will migrate to this set up.