What are the best ways to tune multiple parameters?
Generally people perform a grid search, which in its simplest "exhaustive" form is similar to Method 1.  However there are also more 'intelligent' ways to choose what to explore, which optimize in parameter space in a fashion similar to how each individual model is optimized. It can be tricky to do greedy optimization in this space, as it is often strongly non-convex.

This page describes the basics of optimizing model parameters.