I started reading basic grammar of Japanese, and found this sentence:
I like cats.
I thought が is the subject particle, so I supposed that ねこ would be the subject of the sentence. すき seems to mean "like". So I expected ねこがすきです to mean "Cats like me" rather than "I like cats"; however, it seems like "I like cats" is the correct meaning, as another example バナナが好きだ (I like bananas) in the mentioned dictionary entry also has the same structure.
I asked another learner and got this phrase (私は)猫が好き as the full version of ねこがすきです. However, this confuses me even further, because somehow I understand it as "Cats, I like" (and probably "Me, cats like"). And I think no matter how strange it means, it's still a perfectly fine sentence.
How should I understand these two following sentences? Which one means "I like cats" and which one means "Cats like me"?