An FX lens will be perfectly usable on your DX camera - but what Mrinmoy means by these two statements is that;
Compared to a DX lens, an FX lens will be;
a bit bigger and heavier
consequently it will be more expensive
However, in use, there will be some advantages of an FX lens on a DX camera;
the image quality is very likely to be better
the AF (Auto-Focus) may well be quicker
if you ever decide to invest in a FF camera in later years, you won't need to replace this lens
One over-riding 'thing' concerning buying lenses for Nikon cameras such as yours* is to ensure the lens designation (if Nikon brand) has "
AF-S" in the title. This designation tells you it has a focus motor inside the lens.
If shopping for alternate brands; Sigma, Tamron, etc. you will need to check (or ask us here) before you buy, that it also has a focus motor in.
Failure to get a lens with the focus motor in will limit your enjoyment of using the lens enormously, as you will need to manually focus it, which isn't that easy to do, before taking a shot - and make shooting some subjects all but impossible, particularly with telephoto lenses (e.g. ones with a minimum focal length of say, 40mm or more).
* Nikon D3000 series, D5000 series, plus the older D40 and D60 series.
Be especially careful if buying second-hand (off e-Bay or similar) as sellers don't always describe things as well as they should.
Good luck and I'm glad the post above helped.