If you are not especially happy in your current career, talk instead about the career to which you aspire and why.
By leaving the need to win on the tennis court, you might both get what you want. John Gottman, cofounder of the Gottman Institute, couples who have five positive interactions to every one negative are happy and fulfilled.
I would not go into any further details until or unless a relationship ensued.
The previous-relationship discussion certainly can and should take place if a relationship develops; however, discussing your past too soon, especially with great passion (whether that passion manifests as anger, sadness, tears or longing) will give the impression that you are not yet ready to date.
These are indeed the "Big Two"; the subjects that you will initially want to either tread extremely carefully around or avoid altogether.
You can usually get a good feel for where another person is politically and religiously (or spiritually) just by talking to them, however, unless both of you are clearly on the same side of the fence (i.e., you met at your house of worship or at a political party fundraiser), these are hot-button issues that should be approached with great caution.