WordPress MU is a resource-hungry web application. This isn't a reflection on the people who have worked on it or the quality of the code, rather it is more of a side effect of how powerful WordPress MU is. As an administrator of a WordPress MU-powered site, you are giving your users the ability to run their own web sites—something that was pretty difficult for an individual to do even just a few years ago.
You can set up your site and test it on a good shared hosting package. But if you get more than a few users, you'll quickly hit the limits of what a shared host will allow you to do. Really, to run a WordPress MU site that will get more than a handful of visitors, you need a VPS or, ideally, a dedicated server.
Shared hosting packages are relatively inexpensive; however, the low cost is offset by the fact that your site is located on the same physical server as hundreds of other sites. If any of the sites on the server use an excessive amount of resources...