So this is interesting. It's my first time answering a such open question, but I'll do my best.
First of all, you say you're looking for "specific" recommendation, but since you don't know much about classical or where to start, giving you a few pieces would be like handing a glass of water to a kid wanting to know about the sea.
So I'll try to help you finding music that you like, so you can do your own more in-depth research by yourself.
So classical music has a lot of periods, the main ones being
1: Baroque (1600-1750), the beginning of classical music as we know it today, its main composer being Bach. Baroque music is often pretty simple rythmically, and contains a lot of ornementation. It was deeply influenced by chistian religion, especially Protestantism.
2: Classical (1750-1800). Classical period was mostly represented by the allfamous Mozart. Classical music was getting more accessible and less religious. Orchestration got bigger (still twice as small as a medium symphonic orchestra today). But music was still really strict and relied on rules that could not get broken.
3: Romantism (1800-1900). We broke the rules. Composers got tired of strict rules and began composing freely, as a mean to express complex and deep emotions.
4: Post-Romantism (Late 19th century, early 20th). This one isn't often noted on school manuels, but I think it is important. It's basically a transition to the next period. Basically, composers started expressing ideas that went far beyong their own mind (often in an impressionist style) but without getting to "weird".
5: Modern (1900-1950). So here music started getting a bit weirder. Some composers started being more original (with atonality and such), others composed about more depressing subjects (war). Basically there weren't much rules anymore, and composers weren't having it easy.
6 Contemporary (1945-now). I know i said Modern ends in 1950. That's what textbooks say. Officialy, contemporary movement began in 1945, when composer Anton Webern died, but I'll let you look it up by yourself if you're interested. Basically, rules are officially dead. A lot of people don't even recognize it as music. I wouldn't recommend you to listen to contemporary for now, but it surely is a very interesting subject.
Before getting to the actual recommendations, I will just explain some jargon.
Symphony: A piece written for an orchestra (must contain strings, percussions, brass and woods), often in several parts (movements).
Concerto: A piece written for a soloist instrument or group of instrument, accompanied by an orchestra, also in several movements.