Ideally, you want all these expired domains in the same niche but my question is, if I were setting this up myself, would I have to have different IP addresses and thus more expensive hosting or different hosts?
Actually, not really! If you're scaling large enough, be sure to include some other IP's somehow. But that can be handled with simple other steps, like listing the website(s) in a directory, or signature in a forum post, or create a few tweets/x/facebook posts, etc. That is, you can get access to other IP's without PAYING for them, just to make sure to get some other IP's / subnets into the works. That can even be your last step, when everything else is done and your results aren't hitting hard enough yet... it could be that 1-3 different directory listings or citations, which get picked up by Google, is all you needed.