Is it important to have your own laptop or computer when you start uni?
No, you don't have to have one if you're willing to use the library computers and library printers (printing may be expensive). It's more convenient to have a laptop for times when the library is shut, so you can work in your own room and if there aren't any empty library computers (often near exams/deadlines).
You don't need one but its restrictive without one. Apart from meaning you can only work in the library unless you are a proper bookworm you will have little to do when chilling in your room all the time. Its a TV as well when you are at uni.