Which collection type to use?

This is a somewhat stupid question, but if I have the following
requirements (prioritized), what is the best collection type to use:

1) fast traversal (always traverse the entire collection, but order is
currently not important)
2) mutable
2) fast additions
3) fast removes
4) fast finding of elements by a hashcode or some key

HashMap is the best for this, right?

Erkki