Nikon D3100 w/ 18-55 lens autofocus issues?

I bought my girlfriend a Nikon D3100 kit with 18-55mm lens. I opened to play around with it.
I'm happy with the camera but the autofocus is weird sometime, I know its probably due to my inexperience with DSLRs.
I read the manual and learned about all the modes but I still not getting if its normal what it does.
So I try to focus on the lamp at the end of the room zoomed all the way in, I press the shutter half way and the camera starts to focus. At first its blurry, the motor focuses and it passes the crisp image and goes back to blurriness from where it started. When I zoom out a bit and focus its fine.
Would getting a different lens change anything? My simple pocket camera can focus on it no prob.

Any tips on setting that thing up would be appreciated.

Different cameras perform automatic focusing in different ways.

Re-read the manual to learn as much as possible
about the exact focusing protocol in the D3100.

Sophisticated cameras usually have selectable focus modes
(even my Kodak Z915 point-and-shoot camera has at least two focusing modes).
You should get better results with a different setting.

It also depends on what you're trying to focus on. If it's something with not much detail and contrast like a white wall then the camera doesn't really have a reference point and doesn't know how far away the object is and it won't focus.
A similar thing happens if there's not enough light available. It will try to find the focus and go back and forth and eventually give up because it can't "see".

So make sure that there's enough light and that you're focusing on something that has some contrast.