Look at the whole doorway.
The key and cylinder are only part of it. The bolt has to meet the opening in the frame, and the handle needs to work comfortably. If the lock behaves differently with the door open, mention that. Replacing a cylinder won't necessarily solve a poor fit.
New household, old keys.
After a move, you can count the keys you've received, but not every copy that was made. Rekeying changes the key that opens a suitable lock while keeping the hardware. Damaged or incompatible locks may need a different plan.
Make access easy to manage.
A front door, security door and garage entry may have separate locks. Sometimes compatible locks can be set up for one key. A keypad can be useful too, provided someone manages its codes, batteries and backup access.
Choose for the people using it.
Try the inside turn and handle, not just the outside key. Think about children, guests and anyone who finds small fittings awkward. The most useful hardware is hardware the household can operate comfortably.
Review every outside door, not just the front entrance.
Ask whether the existing locks are suitable for rekeying.
Get the owner or manager involved before changes.