First, some resources:
1) List of addresses. C/O the athlete at the stadium.
2) What to get signed? That's really up to you. Base cards from non-glossy sets like Allen & Ginter, Heritage or Goodwin Champions work great. Another alternative is a signature card. The Autograph Card provides very nice and affordable options.
Second, some suggestions:
1) Derek Jeter, Albert Pujols, and Alex Rodriguez are not going to sign for your TTM request. Get over it.
2) Include a short, legible, hand written note. Personalize it by wishing the player luck, thanking them for their effort last year and be polite, please and thank you, still go a long way in this world. Also, these athletes aren't your friends. Use the appropriate salutation, i.e Mr. _______
3) DON'T ask to NOT personalize it. It wreaks of, "I am going to sell this on eBay." Let the athlete decide. Better yet, by asking for it personalized, you actually increase your chances of success.
4) Include a SASE. Goes without saying.
5) The soft Ultra-Pro top-loaders, not the standard rigid ones are recommended. They make it easier for the athlete to remove and replace the card than a penny sleeve and top-loader.
Lastly, if you are attending your team's camp in person (IP):
1) Don't be THAT GUY. You know what guy I am talking about. The pushy guy that asks for multiple autographs from the same athlete, EVERY DAY.
2) Kids first. Period. Yes, an 18- year old is still a kid.
3) Don't ask for multiples and don't ask more than once. Period.
4) If you are getting autos in person, official MLB baseballs are great. You can throw a couple dozen in daypack easily. Shop around, but this is a good price on a dozen.
5) Pen choice. You can't go wrong with a Staedtler.
6) Politeness is even more important in person. Please, thank you and Mr._______
So that's it. Spring Training autograph hunting 101. Good luck and let's hear some of your successes.