Sharpies are the most commonly available pens to use for autographs. They come in a range of options, from fine, retractable pens, to thicker markers. Depending on what you are getting autographed, a Sharpie can be a good pen to use. Thick Sharpie markers can run through pages of an autograph book, however, so it is best to avoid these if you wish to collect autographs on paper. However, with any other item, a thick Sharpie marker will hold its color, and will allow for smooth writing. Retractable Sharpie markers allow for autographs to be written on a variety of surfaces.
Staedtler pens are used within the baseball industry to auto sign baseball cards. The benefits of Staedtler pens is that they can be used on both the card material and paper, as well as on items such as shirts and bats. Although they are rarer than the Sharpie, the fact that they can write on paper without bleeding means that for the hunter with an autograph book, they are invaluable.
Bic pens are ballpoint pens, which are good for writing on paper but not very useful in writing on other items. They are cheap and readily available. However, if you are looking to get an autograph on a shirt or other item, the ink from a Bic pen will not be visible, and may scratch the surface of the item. Ultimately, if you are using only a book to collect autographs, then a Bic pen will not bleed through, and will be a good option.