This is definitely a problem that you haven't studied Qur'an or Ahadith so far. There isn't just Tafsir Ibn Kathir, go to the website
www.altafsir.com. If you can learn Arabic as well then you will have access to a lot of useful Tafsirs from the past. Notably ones like Mujahid, Al-Tabari, Al-Baydawi, etc. Don't take this as a hard task, the more Arabic you learn, the more competent you become at understanding the meaning of the Qur'an.
You definitely should avoid making Tafsir yourself, since there are a lot of conditions to do this and you need to make sure that you have years of experience in knowing the Qur'an first. In other words, you'd have to be a scholar of a high calibre. But that doesn't mean you can't use quotations from scholars and the Ahadith. There are Ahadith which explain the meanings of verses. Although, you will still need the online tafsirs in order to properly understand them.
I really think you should use Qur'an to explain things when you have the resources to. The Tafsirs explain a lot. You need to make use of them when some disbeliever is speaking against it. Learn the Qur'an and Ahadith for some time, become familiar with many different topics. Before you can say you are confident and familiar with the Qur'an, you should make a daily habit of reading it, and not just reading it, reciting the Arabic, reading translation, reflecting on the meaning, and applying it to yourself in your daily life.
After learning a lot of it yourself, you will find many questions. So go to a knowledgeable Imam and ask those questions you ask yourself, and then clear those doubts. Then when you have met with your Imam and he tells you you know enough to be able to discuss the Qur'an, then do so.
Warning note though, DO NOT learn Qur'an for the sake of arguing with others. This has been expressly forbidden in Islam. Learn it for your own sake and your own spiritual benefit. After a certain point, you know enough to research the Qur'an using your knowledge to come up with verses to show to disbelievers you argue with, but do not learn it for the sake of arguing with them. Avoid that and make it a lifelong struggle to understand it.