When would we want to have a market neutral portfolio?

Specifically, if we have two stocks with different betas and alphas, when might we want to create a market neutral or zero-beta portfolio from the two stocks?

Suppose we have two stock we wish to include in our portfolio. Which weights can we assign to each stock within a portfolio to ensure that the portfolio is always market neutral?

In the case of a single option, if we know delta (How?) we can easily make the option position delta neutral (How?).

When should we use the underlying as opposed to just purchasing the number of puts and calls to make the straddle delta neutral?