I don't really support trying to get a broad understanding of philosophy. It's much better to get in-depth with a specific philosopher and then move on to the next, chronologically.

One thing I haven't seen mentioned is that often, Philosophers of a certain generation are building their theses in reaction to the previous generation. So there's a great reason to read Ancient philosophy, starting with the pre-Socratics.

I highly recommend "Retrieving the Ancients". David Roochnik (the author) was my professor for both Ancient and Modern philosophy. Trying to be unbiased here but this is a great introduction to the pre-Socratics and it even connects their ancient issues with modern ones.