We'd get along fine not reading the old testament at all, only those parts which Jesus referred to Himself. In fact many christians hardly even touch the old testament apart from the stories of Noah, Moses and Pharaoh, Samson, David..and that's about it really.
But we'd be missing out on a lot.
The most important parts of the OT in my opinion is the book of Genesis, it really is the basis or grounding for Christ. The next part is the 10 commandments. But actually it's more like 9 commandments if we don't keep the Sabbath.
But the 10 commandments aren't the most important or greatest commandments. When Jesus was asked which commandment is the greatest, Jesus didn't even refer to the 10 commandments. He referred to love God with all your heart and your neighbour as yourself. So I think that part that Jesus quoted, and the 9 commandments (minus the sabbath) are important to know how to live. Or, if we want to add Jesus's two greatest commandments to the 10, we'd have a total of 12 commandments to live by. Or 11, if you don't keep the Sabbath.
The next most important part of the bible is Proverbs and Psalms. Proberbs teach us how to live, and the Psalms are most useful for praise, worship, any time really.
Then the Prophets are important, the ones which point towards Jesus and prophesy about Him. Isaiah , Elijah, are the big ones, and possibly some others I forget.
I don't personally bother much with Ecclesiastes, Song of Solomon, book of Numbers, and a few of the so called "lesser prophets".