在線(網)上買成票以後，我去了大學的音樂廳。

看觀賞古典音樂表演奏會

看 means "see" in the general sense, whereas 觀賞 is more specific for shows/performances/concerts.
Similarly, 表演 = show / performance, 演奏會 = musical performance

我去年在我大學的音樂廳看過了大學交響樂團的表演。

過 and 了 both denote an action in the past in this context, just using one of them would be sufficient (了 is a better choice here because 過 tends to mean "I have already done something" and in this context, "last year I have already seen...")

因為這個音樂廳是一百多年前蓋的，去看表演/去演奏會時可以一邊聽音樂，一邊欣賞傳統的建築。

Relatively minor point: because 表演 can be a noun and a verb, 去表演時 can mean "when (I am) performing" or “when (I am) at the show", to avoid any ambiguity in meaning it's best to specify that you mean the latter.

原來本來，我以為因為演出者都是大學生，所以表演不會很好，沒想到他們真的表現的得非常好。

原來 = turns out ; 本來 = originally, at the beginning
因爲...... , 所以...... is a sentence structure used to express cause and effect.
Beware of the usage of 的 and 得, they sound the same in Mandarin Chinese, but 得 is used to express the extent of things (They performed. How well did they perform? They were excellent)
Side note: you can vary the 好 with 出色 ( = exceptional, used to describe behaviour / actions)

他們所表演的歌曲子是一首很有名的古典歌曲。

歌 typically means song (i.e. with lyrics you can sing), 曲子 = music piece (can be with or without lyrics)
Side note: a potential variation of 很有名 is 家喻戶曉 (literally, known by every household, idiom meaning extremely famous)

我曾經之前聽過了，但是這是我第一次看樂團表演這首歌曲子。

Same as above with regards to 過/了/曾經 (all mean "already/past" in some sense)

我覺得在家聽古典音樂不如看樂團表演，因為看演出者/樂手很有趣，音樂廳的氣氛也很好。

If you are trying to compare listening to music at home VS going to a concert, you can also say 我覺得在家聽古典音樂沒有看樂團表演精彩 to stress the comparison (literally, I think listening to classical music at home is not as enthralling as attending a concert). 不如 is used for comparison but it is typically used in conjunction with 與其.
Side note: some potential variations of 好 = 愉快 (merry), 輕鬆 (light / relaxed), 歡樂 (cheerful)