This is the best time of the year to hunt squirrels in their natural habitat. The late September/early October is when the squirrels are still young and quite careless with their daily lives. As the season progresses, they mature and are better at hiding away from the hunters view. Most people think that if they wait until late October to hunt when the leaves have all fallen, they may be out of luck. Not saying it isn't possible, I am saying that squirrels are intelligent animals and know better. Especially when they hear the loud crumple of leaves beneath the hunters foot.
Right now, as told by a friend of mine, the males are barking a lot. This allows you to hear the calls better and be on guard for them. Also if you do take a shot and know that the squirrel is dead, you can wait motionless for other squirrels to peep out to see what the heck has just happened.
Now, gun wise I suggest using the classic .20 gauge. I have used that all season this year for the first time. If you are a more advanced shooter then a .410 would do the trick. Some people like to use .22, I would recommend using a long rifled .22. Just to be on the safe side. Then there are people out there who just have to use that .12 gauge for everything. All I have to say is, go for it!