Mount Greenwood is a neighborhood on the periphery of the city. Your transportation options for getting downtown are okay. I've never taken the Metra from there, but I had friends who used to live in Beverly and travel to the loop (essentially) for high school, and their trip took an hour and a half. Your other options include taking the Pulaski bus to the orange line and the orange line downtown, or you can take the bus to the red line.
The neighborhood itself is quiet and residential. Expect to be living near many police officers, fire fighters, and teachers (city workers who want to be near the suburbs). But Beverly, Mount Greenwood's neighbor is a bit livelier, and one of the few neighborhoods in the city where residents are racially diverse. Most of the homes are single family. I bet you could find two and three unit buildings as well. Rents will be cheaper than neighborhoods on the north side of comparable safety. I have to say that the biggest draw back of this old, tree-lined, and quiet neighborhood is its lack of transportation options.
Students at St. Xavier, I've gathered, usually live in the suburbs and travel to school by car.
Hope this helps.