Rechargeables are not a smart buy in this case.
Rechargeables are good for high-drain devices where the quick discharge and amount you use them makes it desirable to have a high capacity batter that you can keep filling up. They do have downsides, however. They are much more expensive than alkalines, and more importantly, they don't have a long shelf life at all. While an alkaline is able to sit for years and not discharge much unless it's used, a rechargeable will self-discharge in a matter of weeks.
So for a controller, the NiMH batteries will go dead on their own much faster than you will drain them.
If you get a setup where you have rechargeables and you can just set the controller back on the charger, that would be ideal. But just regular AA rechargeables, no good.
Edit- That play and charge kit looks ideal.