First of all, congratulations on the new job. Second, it’s a bit hard to answer the question as I’m not entirely sure where your discomfort lies. Does it lie in the fact that it felt wrong to pray for success? If so, rest easy. There is nothing wrong with asking for God’s help so you can do a good job at your job. We could probably all use a little divine help in that area.
If your unease lies in the fact that your friend asked you to pray a Hail Mary instead of some other prayer, remember that praying for Mary’s intercession is perfectly in line with Catholic theology. The Catechism says that “Prayer of intercession consists in asking on behalf of another” (CCC 2647), which is something that most of us naturally do with our friends (think of times that you’ve asked people you know to pray for you). Catholics believe that Mary, like our good friends, is always ready to pray on our behalf. We express this belief during the Hail Mary when we pray, “Holy Mary, Mother of God, pray for us sinners, now and at the hour of our death.” She intercedes for you, just as you might ask a close friend to do.
If you are thinking that praying for your career seems somehow beneath Mary’s notice, don’t worry about that at all. Remember that she was the one who nudged Jesus into performing his first miracle of turning water into wine, presumably because she wanted the newlyweds to have a great party to kick off their married life together. (See the story of the Wedding at Cana in John 2: 1-11). I like that story because it shows that Mary cares about every aspect of our lives, not just what we would call life-and-death issues. I’m sure she’d like to see you happy and finding a sense of fulfillment in your job, just as any caring mother would.