What is a good way to get introduced to the Vedas?

I was thinking about the great works of ancient Hinduism and I realized I really couldn’t think much about them because I don’t know much. I don’t know exactly how to remedy this. Is it a good idea to just go down to the library and pick out a translation of the Vedas at random? Or is there a highly-recommended, annotated, well-introduced translation? Anything really outstanding?

How about the Upanishads? Is there any particular order in which someone should approach the great works of Hinduism?

Try to read the Mahabarata. It is a history really. They also did a movie fairly accurately based on it. I took a lit class that focused on mythology, primarily thorugh the Mahabarata.