Why is sewage coming back up our toilet?

My husband and I just bought a house less than a month ago. We had an inspection done and it passed with flying colors. Almost immediately after we moved in, I noticed that the master bathroom had a bad smell to it, and I noticed the water in the toilet would start to become discolored after it had not been used for a couple of hours. We used only the half bath for about two days. When we lifted the lid of the toilet in the master bath we didn't use for two days, the water had turned brown from sewage. Any ideas what this could be and how expensive it will be to fix it or any remedies we could try before we call the plumber? We have public sewage. Thanks!