But I am not all that familiar with Judaism. What type of questions should I ask them? How should I engage them with the gospel?
(1) You need to be familiar with Judaism, including the various strains of it that you are likely to encounter. You need to go in as a learner first, and find out what they believe.
(2) You need to understand that Jewish folks have endured a long cultural history of assaults on their faith, as well as blatant anti-Semitism, by persons and authorities claiming to be "Christian." As a result, you have less cultural credibility as a Christian than you would have if you were witnessing to a pagan.
(3) In my opinion, engaging a Jewish person with the gospel is simply pointing out how Jesus fulfills the Law of Moses and completes the promises of Abraham. Of course, to do this you have to have a rich understanding of what they actually believe.
(4) Conversion of Jews (or anyone else from a different faith community) takes time. There is also intense cultural pressure not to convert. I have a friend who converted from Judaism about 20 years ago and was disowned by his family for about five years until one of the more secular relatives realized that my friend had not actually abandoned his heritage, just fulfilled it in a different way. He is back in connection with his family, but the relationships are still strained.
(5) I have nothing against Josh McDowell, but his apologetics books are actually quite weak. If you are a believer and you want your faith strengthened, they are of some use. However, if an unbeliever is knowledgable and skeptical, McDowell may convince them that Christianity is not especially deep nor actually answer the burning issues of the soul.
(6) If you are not truly interested in committing yourself a long term discipling arrangement where you can genuinely demonstrate before them a life of stability and consistency where the power of God is active and continuously present (that's what it is going to take), DO NOT engage in evangelism with Jews. You will only make it harder for others. Sending letters, handing out tracts and books, and well-meaning but ignorant claims about Judaism vs. Jesus can be spiritually dangerous for your hearers.