Well, to clear the air....both these are Verio companies. Rapidsite is another name for Verio only.
Before anybody could help you, it would make sense to post your requirements. You would also note that Verio started overselling like crazy during past few months. So, do some searching on the forum and prepare a shortlist of potential hosts.
Verio is a big name in the hosting industry and for the most part you cant really go wrong with them and they are definitely not going to be a one night hosting company and take your money and run away. Though if you want a bit more personal attention / support you might want to look for hosting with smaller companies.
I would say their packages look very decent and fairly priced, overselling or not that's just been the trend in the hosting industry, hopefully you do some research here on WHT regarding the packages as well as contacting them with some questions.
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