What are the best accessories for the Nikon D3100? Ould you like to ask?

Such as flashes, filters and lenses because I'm the new photographer for my job ( I work with pre-teens at a youth activity center and do a lot of photography of the activities the kids do) and I want the pictures to come out as best as they can.

If you were a real photographer 1. You wouldn't need to ask this 2. You wouldn't be using Nikons cheapest camera

Well the camera does what you tell it so accessories aren't part of photo quality. However your knowledge of the camera is. If you're using lots of flash with the kids try this. Set your shutter at
1/200 (flash sync speed) and let the camera decide the aperture. Set your ISO at 200 in the manual setting for ISO and leave it there. Try that and see if you like it.

Also you might want to shoot everything in program. There you should be able to set your focus points to one at dead center. That will give you one point to focus on and not the many the are there in full auto. This will help your overall focus. When using a single point pick one spot, say a child's cheek to focus on, then frame the shot and fire.

Accessories. Well let's see. I think of things like a good bag. This is mine.
http://tamrac.com/5606.htm

A tripod of you need it. Filters? A UV filter is a good idea. It won't effect your photos at all but is a
great protector of that all important first lens element so think about that.

Always use your neck strap - always. My cameras are never out of their bag unless that strap is around my neck - never. Do not allow others to handle or shoot with your camera - never. It's been said that "no one carries a soldier's weapons" - no one.

When you're between shoots, a lull in the action, turn the camera off - it saves battery power. Do you have extra batteries, perhaps even an extra charger? If you're shooting a lot extra batteries and
memory cards can be important. What cards do you use? Class 10 at 8gb seem to be very popular and work very well… And they're fast. I always carry 3 in my bag.

There's probably other things as well - oh, just thought of something. I always carry a large size women's make up brush in my bag. It's very soft and excellent for quick dust offs when starting a shoot. You pull your lens cover and notice little dust particles on your UV filter give it a quick brush off with that brush - it works just great. Then there's the micro fiber lens cleaner - carry one of those as well.

As I say there's probably other stuff that's not coming to mind but that's a start. Good luck and have fun with the kids, I always do.

I carry my Nikon DSLR in a generic back pack with towel wrapped around it. I'm not saying you should do same but to buy a Lowepro or Tamrac camera bag you are just advertising to thieves what you're carrying.
Definitely a filter to protect your lens.
If you're shooting a lot indoors, a flash Might be something to buy. In available light without flash, will probably take some experimenting as far as ISO setting. It's great if you can shoot at ISO 200 with acceptable photos, but you may have to experiment between 200 and 600 ISO.
You never mentioned what lens you have but another lens would always be desirable.

The very first accessory you should get is a good book about the basic principles of photography. From there you would know what to buy next.