What does koto mean?
In context I'm looking at "Anata no koto ga suki da." I've figured out what each word means except for koto. I'm guessing anata no koto means your or something like that? There's just too many entries for koto in my dictionary...

Question

Answer

koto means thing. its not an object that you can touch though, that would be mono.
it can mean the thing of....
anata no koto= the thing of you/your way/your manner.
yomu no koto= the thing of reading/reading

Answer

"-no koto" means nothing but emphasis. "anata ga suki" and "anata no koto ga suki" are the same.

Yomu is verb. "yomu koto" is OK. I'm afraid "yomu no koto" is wrong. We never say like this. Nouns always be suffixed with -no then anata-no koto is OK.

"anata ga suki" also means I like you romantically or I love you.
The nuance of statement "suki" depends on the situation ... It is true "-ga suki" does not sound so romantic. However the topic here "anata" itself states something romantically that if you say "anata ga suki" implies something romantic while "-ga suki" does not sound romantic.

"suki" alone still sometimes romantic ... for example when you say "suki" face to face with your lover, it's most romantic word in terms of Japanese.

Answer

Anata no koto ga suki da. = I l ike you (romantically).
The expression here requires "koto". 
To tell you the truth, I don't know why. But if you said: "anata ga suki", it doesn't mean "romantically".
If you like your friends at school you say: "suki".
If you like the hot girl next to you you say: "~no koto ga suki."