As you use your camera more often, you’re going to need storage for your photos and your equipment itself. It’s a good idea to invest in some larger memory cards, which are selling for much cheaper prices than they used to back in the day. We personally use an 8GB SanDisk SDHC card with our Nikon D5000, but a 16GB card or larger can also be quite handy. Nikon has a list of approved memory cards that it has deemed compatible with the D3100, so the choice is ultimately yours.
As far as purchasing a camera bag, it might not be necessary for you to invest in one right away, depending on the options you have available. But you want to make sure your camera is well-protected, especially if you find yourself on the go with it a lot.
There are some budget options out there: Nikon has a starter SLR camera case for $27.95 on Amazon, and Lowepro sells a variety of bags and cases that may fit your needs. For a more aesthetically pleasing (if pricier, at nearly $200) look, the Billingham Digital Hadley bag might be right for you. Most of these bags have space for an extra lens or two, but you’ll have to decide what’s best for you as your equipment expands.
If you’d like to toss your camera into a large purse or backpack instead of an actual camera bag, you may want to consider the Nikon CF-DC1 Semi-Soft Case, compatible with the Nikon D3100, for a little added protection. This particular case will hold the camera body, along with a lens up to the 18-135mm Zoom-Nikkor. Lens pouches can also always be purchased for your other lenses.