In general there are three types of grip strength:
Crushing: This is the type of grip one normally thinks of. Shaking a hand, closing a gripper etc.
Pinching: Pinching strength is mainly reliant on the thumb. Imagine picking up a textbook by the binding, that’s a pinch grip.
Supporting grip: This is a “holding” type grip, as one demonstrates by holding a loaded barbell.
Training each of these aspects will lead to the strongest overall grip. Holding a disc is some combination of these depending on how you grip.
As rehder stated, start with the #1 CoC gripper if you don't already train your grip. If you can't close it try working on using two hands to close it, and the try to keep it shut with one hand. This is called a negative and will help you progress towards closing it.
Forearm strength will develop some as you train your grip but direct training will help your grip and overall ability to use your strength. It is also beneficial in everyday life. Levering is the best overall forearm strength exercise. A good guide is located here: http://www.sherdog.net/forums/f13/lever ... ng-813568/
Levering is basically holding an elongated object that is weighted primarily at the far end from your grip. Then you just try to move it around in a controlled manner. I.e., hold a sledgehammer at the handle straight up in the air with your arm extended and lower it slowly away from you, then return it to upright. Repeat.
As with any training, it doesn't matter how much you can do today, it matters if you can progress over time. Don't kill yourself going overboard, just do a little more each time. Success will come.