There is a big Staples and a Costco on the edge of Leeds City Centre, both walking distance from the University.
There are also a few big Asda/Walmart stores in the suburbs.
However, Wilkinsons is cheap and cheerful (a little bit like Target, but not as good!) and it has a large branch in the City Centre, and you'll find most of what you need there.
You will find there isn't very much big box retailing here, compared to the US. Most shops are 'in-town' and much smaller than you may be used to, but that's all part of the charm in my opinion, but possibly part of the frustration for some!).
Welcome to Leeds, where we are enjoying a beautiful sunny day today!