Measure the width and the height of the apartment entry door if you have your own furniture. In addition, you should make an agreement with the apartment owners about the rental cost whether it includes costs of electricity, water supply, security or not. This to anticipate more cost you should pay monthly.
Beside that, you can ask some questions to the apartment owner, like the electricity, the water supply, the sanitation, and the apartment construction. The careless apartment checking will endanger your budget. If there is any cracked floor and wall in each rooms in apartment, you can request the apartment owners to repair them. You can also feel the apartment condition, is there any unexpected smoke such as high noisy or sunlight access inside.
Then, take some notes and pictures of each apartment you visit. It is the great way to check more detailed the objects inside the apartment. You can open the doors, the wardrobe doors, and the drawers. Or, you can switch on the shower and the lamp whether they run well or not. Within this ways, you can compare objectively one apartment with the others.