I personally witnessed all 3 autographs at a baseball card show nearly 15 years ago. I actually have a picture of Mickey Mantle and I shaking hands. All 3 autographs are very legible on the baseball. Just curious as to the possible value of something like this.

I can tell you that each of these hand signed signatures on a baseball by themselves is worth more than all three on the same ball. This is another case of the components being worth more than the whole. I believe the MVP Fan For Life is close on his projected value of individual signatures for the three players but all three on the same ball would have a value of around $500 in the market today. And this is only provided you have all the support information you stated and the ball is in as good a condition as you say it is.

well mickey himself is $500. reggie is $100 and whitey is $125. so on the same ball it would probably be $800

$150 to $300 , Depending on the buyer and how it is sold . I think if you advertised it for $200 , or a $200 Buy it now price on eBay you would get it .
Book values are extremly overpriced . Check out the sports collectible sales on TV . The will offer you an $800 deal for only $325 when they know they could only get $225 tops for the item on eBay . Of course therer's lots of inexperienced people out there that think they could get $800 for the item and rush to buy them . Then they stick them on eBay without a reserve and wind up getting $89 . Check eBay.com for similar items .
Check out :
http://cgi.ebay.com/Lithograph-Autograph...
And :
http://cgi.ebay.com/Mint-Mickey-Mantle-A...
I have a 1953 framed document with Mantle , Ford , Martin , and 4 other Yankee players . It is sitting in my store for $500 firm . Baseballs in good condition are worth more than average documents , but "card show balls" are worth about the same or even a bit less .
Kovels Antiques and Colletibles book lists a Mantle & Ford signed ball sold for $285 in 1999 . This would be a top price . Values today are about the same as 1999/2000 , maybe $20 more on this . I would add $45 to the value for Reggie's signature , bringing the total to $350 . But remember that is a top price and may be hard to get unles it sits in a store for awhile . If you need to insure it , I would get it insured for $400 .

I would pay $750 all together for it.

Check with Jack Heir, a collector of autographed baseballs for over 50 years.