Small cash rewards are a good idea, they have this in Hattrick as part of getting your managers licence. It will have little effect on the top teams but for new teams $10,000 here or there could be important.
*Obtain a triple double in a league game
*Expand your arena past X number of seats
*Sell a player for over 1,000,000
*Have a U21 player from your own nation
*Collect X number of scrimmage flags
*Have X number of positive PD in a single season
*Place a player in your Hall of Fame
*Win a match with each defense at least once
There is nothing wrong with these but for new players most of these are unthinkable and very long term goals. They are fine as achievements but initial ones should be stuff like:
Sell a player
Buy a player
Win a league game
Score 100 points in a league game
Keep an opponent to 50 points or less in a league game
Buy a staff member
Play one of your draft picks in a league game
etc