If you are on a county or municipal water system, just put an in-line carbon filter under the sink. (Brand is Culligan, very inexpensive from Amazon) I did this and ran it to a drinking water faucet mounted in the kitchen sink surround. Taste is excellent.
If you are getting your water from a well or cistern, you might like to do the purifying routine, and then finish with a carbon filter.
Just re-read and saw you are renting. Go with a Brita pitcher. They have large sizes available.
he can’t modify the plumbing, he’s renting.