Arbitration is available to anyone with 6 or less years of service once they've been promoted to the MLB level. You'll usually have 3 years of an entry level contract, and then 3 years of arbitration before they're eligible for free agency-- unless the numbers they put up dictate they deserve more money from arbitration, at which point you may find it more beneficial to lock them down to a contract for years past the point where they will become a free agent. Doing so may ensure you get more value for the player's presumed production, and it will also make them tantalizing trade bait should you ever decide you no longer need the player as they will be cost controlled for years to come.
I tend to offer arbitration to players who are progressing along in their development as expected, and to players who are organizational filler or whom I don't care very much about. Once a player has a career year, or is approaching free agency, that's when I tend to worry about the future of the player in the organization and where they fit into my finances. If I deem them a crucial component of the team, then I do anything necessary to lock them into a favorable contract for the club. If not, then I usually try to trade them for younger prospects of equal or greater value before they hit free agency and I would be forced to let them go for no return.
That's the last thing you want is to get nothing for players, no matter how little they may contribute to the team they can almost always be turned around for something of some value somewhere else in your organization. --- SURGEON GENERAL'S WARNING: The preceding post is tainted.