If you have not used a gaming mouse yet then you are in for a bit of a learning curve.
part of increasing your cast and action rate is teaching the muscles of your right hand to click and push buttons on a gaming mouse.
If your favorite game ( and mine is World of Warcraft) you will find that there are keybinds and macros that you can use along with a gaming mouse that will allow you to output more actions like healing or damage much much faster.
You must trust me on this. It will be a process, since you will need to teach the muscles on your right hand to instinctively hit certain keys on the right hand mouse. Look below at a typical gaming mouse, The Razer Naga.
I count at least 14 buttons for your index and right thumb.
Keeping track of which button is keybound to which ability will be a process. BUT once you master it you will be casting and doing actions with both your left and right hand. If you are a lefty Razer has lefty specific mice.
Bottom line you will need to make use of your keybinds and to retrain both hands to cast and do actions as fast as possible.