docs: Consolidate getting started guide and remove duplicated examples (#658)

There are some examples that are duplicated in the getting started guide and in
the examples folder itself. This commit removes the duplicated examples and
updates the getting started guide to include then from real source files that
are passed through the linter and have tests.

Co-authored-by: Diego Hurtado <ocelotl@users.noreply.github.com>
Co-authored-by: alrex <aboten@lightstep.com>

Author: 3 people