If someone told you to start with Mahābhārata, I think they were pulling your leg. You will have to take notes just to follow the plots.
The Bhagavad Gītā is often where Westerners will start. It is, in fact, the most read portion of the Mahabharata. However, even this can be somewhat difficult without an understanding of the culture and time for whom it was initially written. On the other hand, reading it will give you a much better understanding of the culture.
You will learn key astika (Hindu) concepts such as mokṣa, or liberation—as well as the interplay of the three guṇāḥ (qualities), namely constructive harmony, passionate confusion, and destructive chaos.
You will also see the multiple ways one can practice Sanatana Dharma (Hinduism). The Gita synthesizes Jñāna yoga, intellectual self awareness ("know thyself"); Bhaktí yoga, practicing loving devotion (worship); and Kárma yoga, working or acting without expectation of personal gain (selfless action). Through these one can liberate oneself. It doesn't claim there is a solitary path to liberation, but some paths are easier to trod for you than for me and vice versa.
Perhaps the key concept you will learn is dhárma, which I hesitate to define here. In fact, the story begins with Prince Arjuna feeling conflict between dharma to his country and people as a warrior-leader and dharma to his kin whom he faces on the battlefield. The majority of the text that follows has śrī Kṛṣṇa advising and answering the queries of Arjuna. We learn that living our dharma not only brings us closer to God—however one wants to define that—and our own liberation, but can also inspire others to live their dharma.
Because it is important, but doesn't come up in many translations, you may also want to look into the concept of līlā (play) before reading. Regardless, all of the above concepts will come up in one way or another in the Gita and will make it much easier to understand other South Asian texts, such as the rest of the Mahabharata. That's why it's such a great introduction!
I recommend the translation by Winthrop Sargeant. SUNY made a pocket version of his translation which I often carry in my purse. I am a big fan of writing in texts as it helps me connect the content to other things I have learned. And, as I grow over time, it is interesting to see how my metaphors in my notes change. Along the same lines, during your first read through dog-ear anything that went right over your head and then you can later search for a different translation of that section and see if that clarifies anything.
I also highly recommend starting with a version that lacks commentary. This allows you to form your own thoughts about the text. Later, you can see what others have said. But your first time with anything only happens once, so see what clicks for you without commentary.