Isometric embeddings of $c_0$ into metric spaces

Question

Are there any nice and useful criteria or theorems which assert when a given metric space $M$ contains an isometric (not necessarily linear) copy of the Banach space $c_0$ or its unit ball $B_{c_0}$? (I assume that both $c_0$ and $B_{c_0}$ are endowed with the supremum norm). I am especially interested in results for the following classes of metric spaces $M$:

1. arbitrary metric spaces,

2. Banach spaces,

3. Banach spaces containing closed linear copies of $c_0$,

4. Banach spaces containing complemented closed linear copies of $c_0$.

I am also interested in particular subclasses of the above mentioned classes.

(Example of a result I like: if for a compact space $K$ the Banach space $M=C(K)$ of continuous real-valued functions satisfies (4), then it contains an isometric complemented linear copy of $c_0$.)