I particularly enjoy Dvorak's symphonies, my favorite being 7 and 8. I also enjoy Prokofiev specifically Lt. Kije, and his Suite for 3 Oranges. I second all recommendations to break down the very broad category "classical music" into its component eras, explore each, and start to figure out which ones you like. I am not very big on Mozart for instance. That doesn't mean I don't think he is brilliant but I kind of find Mozart boring. If you are attending a university odds are very good that uni has a music school or department. If so, then odds are extremely favorable that the uni music department hosts regular music performances, maybe as frequently as on a weekly basis or more. (When I was a music major we were required to attend x many concerts every semester. To help us achieve this the uni had weekly performances/master classes/etc for free every Friday. I learned the most I've ever known about jazz, and gained a lot of respect for it, during one of those sessions. Every session was free.) Besides those performances (visiting musicians etc), you will have bands (symphonic, drum, brass, etc) that music students at the uni are a part of, which will put on their own performances throughout the year. In addition you will have junior and senior recitals (usually at the end of the school year) which are always free, open to the public, and have refreshments (sometimes free wine!) afterwards. On top of all that don't forget the chorus and vocalist performances. I think that if you sought out these experiences it could be a fun and cheap way to start listening to a lot of broadly considered "classical" music. Usually junior and senior recitals try to showcase each musicians' abilities and talents across genres so they will probably include pieces from multiple different eras or centuries. Keep the programs, draw stars next to the pieces you particularly like. I heartily encourage you to take a class on the history of classical music, I think you may find it really educating and satisfying for some of the questions and curiosity you seem to have.
You were spot on about the masters classes and performances. The music department is a whole other school, so I wasn't aware of just how many events they jave. To my delight I've found out they are actually performing "Cosi Fan Tutte" at the end of January which so far is a real favorite of mine. The only thing that really makes me sad is I graduate next semester and I feel like I've really missed so much. Working two jobs and going to school full-time robbed me a bit of these experiences. Well thank you for the recommendations, and I will hopefully use what time I have left to take advantage of these opportunities.
You may be able to attend for free as a local community member (depends on your uni) but that would be impacted by any work schedule you have. Yeah, since I was once a music major I get to know about a lot of cool resources generally available to those programs :) They should definitely have a class on the History of Western Music or something which would cover Classical, Baroque, Romantic, etc. Good luck, I am pleased that serendipity won the day and you will be able to see Cos Fan Tutte in person.