Feelings

心 (xīn) is the heart. It is also the mind, and Chinese has never separated the two the way English does since Descartes.

Once you can spot it, a whole family of words opens up. 开心 (kāi xīn) is happy: an opened heart. 担心 (dān xīn) is to worry: a carried heart. 小心 is careful, a small heart. The character is doing consistent metaphorical work, and it is the single most useful component to recognise at this stage.

The many ways to be happy

Mandarin has four common words where English mostly has one, and they are not interchangeable.

高兴 (gāo xìng) is pleased, in the moment. It is what you say on meeting someone.

开心 (kāi xīn) is cheerful, having a good time. Lighter and more colloquial.

快乐 (kuài lè) is happy in the greeting sense: 生日快乐 is happy birthday. It appears in wishes far more than in descriptions.

幸福 (xìng fú) is deep contentment, the happiness of a life rather than an afternoon. Using it about a nice lunch would be strange.

喜欢 does most of the work

喜欢 (xǐ huān) is to like, and it is the verb you will use constantly. It covers liking a thing, liking a person, and enjoying doing something.

爱 (ài) is to love, and Mandarin uses it more sparingly than English does. 我爱你 (wǒ ài nǐ) is a serious statement, not a sign-off. Among family and friends it is said far less often than English love you, and its weight is correspondingly greater.

Anger is generated

生气 (shēng qì) is to get angry, and it is literally to produce 气 (qì) - breath, air, vital energy. Anger is something you generate rather than something you are.

That is the same instinct behind 客气 (polite, guest-energy) and a dozen other compounds. 气 is the second component worth learning to spot, after 心.

讨厌 (tǎo yàn) is to dislike or find annoying, and it is much commoner than 恨 (hèn), to hate, which in Mandarin as in English is a strong word.