A rented kitchen comes with rules you did not write. Before you buy anything, find out what the lease and the landlord allow, because that answer narrows the filter choice more than any product feature will.
Get the lease terms in writing first
Ask the landlord whether you may drill a hole for a new faucet, cut or reroute supply lines, or mount a housing to the cabinet wall. Ask whether the original faucet can be removed and stored, and who keeps it. A short email reply is enough. Keep it with your lease.
Measure what is actually under the sink
Take photos of the existing supply shutoffs, the drain trap, and the cabinet floor before you start. Measure the open width and depth of the cabinet, then subtract room for the door to open and for a person to reach the cartridge. A housing that fits the cabinet but blocks the door will be a problem at the first filter change.
Check the faucet too. Note the spout type and whether the aerator has a standard thread. Some diverter and mount options depend on that thread, and a mismatch means a second trip to the store.
Choose a format that installs without cutting
If drilling is not allowed, a pitcher or a faucet-mounted unit may be the only fit that does not change the building. Under-sink systems that connect to the existing cold line usually need some plumbing work, so confirm that step with the landlord before you order. If the building shares a riser or the water comes through a common system, your choice of whole-house equipment is not yours to make.
Plan the exit before the first install
Decide now how the equipment comes out. Keep the original parts, the mounting hardware, and the receipt. Take a photo of the finished install so you can show the landlord what was added and what was removed. If you leave the filter behind, write down what was left and where. A removal plan is part of the fit, because a rental that cannot be restored to its starting condition can cost you the deposit.
Confirm the local ratings before you choose
The site's county report card shows the local water picture, which helps you decide whether treatment is needed at all and what to look for in the water data. You can read how the grades are built on the methodology page.