The New testament is a fulfillment of the old testament. There is a lot of context and history in the old testament which Jesus references. Still, the the new testament can be read alone.
You can read Old and New Testament as their own, but reading the Old Testament first will give you insight on some references that are made in the New Testament as well as the context as why Jesus is very important through out the New Testament.
Especially when it comes to Jesus' lineage and other prophets of the past that has spoken and prophesied about him.
Honestly NT feels more like the actual game rather than OT, cause heck with the amount of build up of prophecy in OT and fortelling of Jesus it even made OT feels more like a Prequel that tries to explain why Jesus is so important.
I suggest starting with the Old Testament and then reading the New Testament just because of how helpful it is with the backstory, history, culture, and prophecies. On BibleGateway.com, you can read it in any translation available and hear it as an audiobook if you need an online or app-based source.
Does the NT contain verses of the old? I'm quite interested in the teachings, Genesis, Psalm, Mark, Kings... If from what I'm understanding in this convo, I think I should read OT and consider NT if have the time
Old Testament is a lot of battles, poetry, music, proverbs, Laments, prophecies about the coming of the Messiah, and one horny duet while the New Testament is the life of Jesus, the Messiah fulfilling the law, and how the church should live as followers of Christ.