This will get you started...
Q: When does a player become eligible for salary arbitration?
A: A player with three or more years of service, but less than six years, may file for salary arbitration. In addition, a player can be classified as a "Super Two" and be eligible for arbitration with less than three years of service. A player with at least two but less than three years of Major League service shall be eligible for salary arbitration if he has accumulated at least 86 days of service during the immediately preceding season and he ranks in the top 17 percent in total service in the class of Players who have at least two but less than three years of Major League service, however accumulated, but with at least 86 days of service accumulated during the immediately preceding season.
To answer your other questions:
I think it is near the top of the list of factors and how close to the top it is depends on the greatness of the need for the player, the pressure on the GM to win now and the likelihood that putting him in the lineup sooner, rather than later, helps the team win.
As a fan of a small-market team, I'd rather see the team go slowly in bringing prospects to the big club, especially when they're likely to be great players. The more of a player's best years that the small-market team gets, the better, because they'll have to open the wallet wide to keep him if he turns out to be great.