Choosing which type of flour you want is up to you.
Both types of flour are all-purpose, which means they're equally good for making most baked goods. The difference is that bleached flour has been made chemically whiter in appearance than unbleached flour.
The bleaching process does compromise some of the flour's nutrients, but they are often added back to the flour.
Which flour you choose is a personal preference. Some bakers like their white cake and bread as white as they can be; others prefer their flour to be processed as little as possible.