I wouldn’t be to concerned from a privacy perspective since you will be in control of the modem and router. I would be concerned about it from a cost and flexibility standpoint though. Typically landlords are not in the business of doing their tenants favors. If they are offering this, its because its a benefit to them.
Verify the details with your landlord what they will charge you vs what you could get by handling the ISP account yourself. Since you are already responsible for getting the modem / router its not like the landlord is doing much for you. Make sure they are sending you copies of the ISPs invoice if your landlord is going to bill you separately.
Also see what kind of internet plan they plan to purchase and what your options will be to change it, if your needs change.