Object pronouns

I've managed to get myself confused about using object pronouns in some cases. I'm unsure whether it's correct usage, or incorrect, but very common, usage

Q: Who is hungry?
A: Me
or should it be:
A: I

If I put a verb in ("I am"), then it's obvious, but without the verb, "I" am still the subject of my answer "I" am the one who's hungry. So, is "me" or "I" correct? If "me", then why? (I'd say "me")

Or "The worst player on the football team is I" or "... is me"?

Again, I'd say "...is me", but I think it should be "...is I", because the verb "to be" is intransitive so doesn't take an object". But "...is I" looks wrong...

There are similar cases where "is I" looks more correct (eg "it is I who is confused" - although now I'm thinking should be that be "it is I who am confused"? Argh. I'm even more confused!). Even in that case "it is me who's confused" would be common.