The first question which comes to mind is, "what are the aspects the different characters have?"
I ask because Fate point awards (and usage...) revolve all around Aspects essentially.
As an example of one of the games I ran at a convention, the group was composed of (Pure Mortal) Psychology students at Yale University. One them, with a High Concept Aspect of Prissy Brain, had another aspect of Magic Isn't Real, which was getting awarded Fate Points left, right and center because any time the character saw anything "out of the ordinary," the player would roleplay the character as though there was a perfectly logical explanation for what they saw/heard/felt/smelled/etc. In fact they did such a good job that I didn't even need to compel the aspect, the player did it all on his own.
As an example of an aspect which I plan on using for a character at some point is Once an Eagle Scout, always an Eagle Scout.
Given the nature of it, it can be used to have just the right item if/when needed (that whole Be Prepared thing...) and can help boost Survival, Guns and Scholarship rolls due to various merit badges earned, first aid training, etc. By the same token, a character who is an Eagle Scout could be expected to always "Do the Right Thing," even if it is not to the benefit, or possibly even to the detriment of the character, i.e. if an Eagle Scout found a wallet containing $1,000 (which could provide a temporary Aspect of Sudden Windfall) the character could refuse to keep the wallet & money and instead turn it in and/or find the rightful owner, thus acting true to their nature/Aspect and earning a Fate Point. Or the Aspect could be Compelled, by the GM stating that rather than spending time with friends, hanging out, etc. the character volunteered to help fix up or clean out a derelict home, church or other public building and thus providing a hook to get the character in trouble...
In short, it really depends on the Aspects people have. Using the text in the book, people might only have rather bland Aspects, toasty or Fuego! The more interesting the Aspects are, as well as the more open-ended by having double (or more) meanings, the easier they are to be used by the players as well as the GM.