Use your university cluster / super-computer for the analyses. For storage, if is just you (as you did not mention anyone else), a couple of external hard-drives with redundant copies of your data and kept on different locations should suffice for safe storage.

Now, if my answer is completely off the mark, provide more details about your usage: volume of data, how many samples, how many users, is it a small one-person or lab project or a large collaborative effort, and so on.