There are many reasons why you would contact your senator or House or Representatives member. If you have an idea for a bill the House and Senate could initiate the idea. On the other hand if they were going to voting pass a bill on increasing taxes in Illinois you could get in touch with them to tell them to vote against it. Here is a link to get in touch with your federal Senator or House of Representatives member.
There are the same reasons as before to contact your Illinois General Assembly Member. Make sure if it is a state issue you contact your Illinois General Assembly but if it is a Federal issue you contact the Senate or House of Representatives. Here is a link contact your Illinois General Assembly member.