Security for user-uploaded data

Hello I am an r-shiny newbie!

I want to make (and put on the internet, probably hosted on shiny.io) an app that can take a user-submitted csv file (with a certain format that I will communicate to the user) and let the user play around with filtering, disaggregating and visualizing that data. I was planning to use this example as a model for the letting the user upload data: 9.1.3 in the mastering rshiny guide.)

My question is basically, if my app allows users to upload and manipulate their own data set, how secure will that user's dataset be / what are the steps I would need to take to ensure its security? One follow-up question I can think of is: Can the dataset only be stored for the duration of the user's visit to the webpage? But generally speaking, I don't know what I don't know when it comes to security, so there is no risk of over-explaining!

I do not know much at all about cybersecurity and am trying to determine if I will be able to figure out how to securely/responsibly host this app online will on a relatively short time frame. It seems really nice to let people use the app for its intended purpose (disaggregating data) without the barrier to entry of them having to download R and compile it locally. The data this app is intended for is sensitive: it is college course records (presumably de-identified by the registrar first, but still there's grades and stuff in there), so I don't want to mess this up!

Thank you!!