If you are not familiar with the skeletal story of the Mahabharata, just read the first sections of each chapter. Then, once you get the gist of the story, come back and read a few of the myths that go into the main story. Then, read the myths that those myths link up to. When you are feeling adventurous, go to the Table of Contents and click on a random link. You are guaranteed a good story wherever you start.
If you are a glutton for punishment, or if you want to read the story as a linear narrative, just keep clicking on the Next button and reading the next section. The reason I don't recommend that method is that you might miss most of the aura of the epic. You might even lose the thread of the story! In fact, you will often find the digressions more interesting than the main story. You will find many of them self-contained. Oftentimes, you may have heard the story before, just not known it was part of the Mahabharata.
This story is not meant to be read in one sitting, from start to finish. You are not meant to untangle the tangled threads of parentage and lineage, of who fathered who and who is whose heir. The reason these nice folks are fighting a war is because everybody alive then had different opinions on these niceties. Instead, the story is meant to be discovered in pieces. Start wherever you want, and go where your fancy takes you. Then, maybe, you will understand why Indians have loved the story of the Bharatas for thousands of years and why the story has taken root wherever in Asia that it has traveled.
Enjoy.