What lens should I use with Nikon D3000?

What lens should I use with Nikon D3000? There are so many choices, but I'm little bit confused with the compatibility. Just found that AF-S lenses are compatible with this model. What about DX? Do I have to look for this feature (DX) along with AF-S feature as Nikon D3000 has a DX (cropped) sensor? What will probanly happen if the lens isn't a DX one?

Http://www.kenrockwell.com/nikon/compatibility-lens.htm

You'll have to use AF-S or AF-I lenses to maintain autofocus compatibility. You can use other F-mount (AFand AI) lenses but you'll have to focus manually. You don't specifically need DX since your camera has a crop sensor. Full-frame and film lenses will work perfectly with yours.

http://keerok-photography.blogspot.com/2011/05/lenses-so-many-of-them-there-is-no-best.html

You want a Nikon AF-S or a sigma HSM or a tamron with built-in motor. DX is not that relevant.

Before you choose a lens, ask yourself what your 18-55 kit lens is not doing for you.

If you already have the 18-55mm lens which should be included in the kit, then get a 55-300mm lens, so this way you cover a range of 18-300mm, the 55-300mm is cheap and has very sharp details