You need to learn both. Even though on-yomi comes from Chinese, it is used daily in modern Japanese. To give an example, you can't say you don't want to learn any word of French origin when learning English. Just because words like "pronounce,' 'example,' 'university,' 'lunar,' and hundreds of thousands of words are from French doesn't mean a leaner of English does not have to learn them. These French words are absorbed into English, just like words using on-yomi are of Chinese origin but are now absorbed into Japanese. So you'll have to learn both! :)

Both readings are necessary, but learn through words and not individual kanji.

i'll just add an example of how both readings are used in daily japanese: the kanji charachter 「新」 1- kunyomi: atara 新しい　: atarashii =new 2- onyomi: shin 新幹線　: shinkansen = bullet train

You'll have to learn both!