When getting something signed, you would want it to be valuable and hold it's value for awhile. Whenever I am getting an autograph, I think about what the player is worth. If it's a superstar I will contend to get an item that is usually higher end such as a Jersey, bat, or a ball. If the player isn't as good I will look to get a card signed or something flat such as an 8x10.
It all depends on preference, but if you don't have a lot of money, use higher end items to get higher end players. Make sure to use a good sharpie on Jerseys and balls. Except for baseballs which should always be signed by a pen, Jerseys and other balls will hold the signature better if signed by a sharpie or paint pen. Cards are also better served by getting signed by a Sharpie. Sharpies will bleed on baseballs so that is why I don't use them on that kind of surface.
If going to a game and you need a lot of players I suggest using a binder to hold all of your photos and sports cards as it is easier to find what you are looking for. When everything is organized it is much easier to get the item out and get it signed before the moment passes with the particular player.
So all in all, weigh your options before you get an autograph, if it's Michael Jordan get a jersey signed! If it's Tyler Clippard get a card signed and save the ball or bat for another star player.http://sportsandcelebrityaddresses.com/free-autographs/