"They mean a lot to me."
Translation:Zij betekenen veel voor mij.
Does zij imply just people or also inanimate objects, like 'they are tasty.'?
We use 'zij' to refer to people in Dutch. For inanimate objects, use 'ze' instead. In written language, 'zij' can be used. However, I'd recommend to use 'ze' to keep things easy for yourself, and it's the natural way to speak. Read about it here: http://taaladvies.net/taal/advies/vraag/939
In English, "mean" as a verb signifies two different things, and they get two different words in Dutch. To intend something is "bedoelen." I remember this by noting that "doel" is the word for "goal." "Bedoelen" is to have something as a goal, to intend it. To signify or represent something (like a word definition or a value to me) is "betekenen." If you remember that "tekenen" is "to draw," then you might be able to remember that relationship. To draw something is to make a representation of it.
So here, do they intend a lot to you, or do they represent a lot to you? It's the latter, so "betekenen."