What To Get Signed
Always try to use the Official Major League Baseballs.
These balls are leather and typically cost around $12 each. Before they started using the same ball for both leagues several years ago, they used to have different balls for the American and National Leagues. Each ball was imprinted with the signature of the respective League President. So, it was always best to have a player sign the ball that was specific to the league he played in. For instance, you'd have Hank Aaron sign a National League ball and Mickey Mantle sign an American League ball. Now that there is only one ball for both leagues (imprinted with the signature of the Commissioner), it's a moot point for contemporary players.
Avoid "Official League Balls."
These look like the real deal, but they may have a synthetic cover and cost around $5 each. Signatures on these balls will fade and/or bleed over time.
Use a medium point blue ballpoint pen. Try to find a pen that leaves a nice dark, blue line. Bics with the white barrel are my favorites. Avoid superfine ballpoints that leave a thin weak line.
Why Do Some Baseballs Develop Brown/Yellow Spots?
The leather in the ball contains various acids and chemicals that may or may not turn dark with time.
Baseballs should be stored in a dark and dry environment. But, even under the best conditions, the inherent acids/chemicals in some balls will create dark spots over time. This is a ticking time bomb in some balls and there is NOTHING you can do about it.
In my experience, the dark spots will usually appear in the first 10 years after manufacture. If a ball makes it past 10 years old and has no spots, it will probably remain okay.
This is why I shy away from getting balls signed, especially from today's high-priced signers. Who wants to invest a few hundred bucks in a signed ball and have it self-destruct in a few years?