Remember that just because the system is expensive doesn't mean it's better. For example, Jane installed the Super Duper Alarm 2000 into her apartment. So, the first night it's installed, the cat decides to get up and get a drink of water. If you purchase an overly-sensitive alarm, the results are pointless. Sometimes less is more.
Many security companies offer great protection for under ten dollars.
You might want to invest in something as simple as a door stop alarm. It won't go off when it senses a particle of dust, or if someone comes within two feet of the door, but it will emit a shrill alarm when the door is opened and pushed over it. This alarm can be set to scare off unwanted intruders, or to chime to notify you of incoming visitors. You can take either alarm with you when your lease is up. Keep in mind that most burglars are looking for an easy place to break in.