My daughter has the Nikon AF-P Nikkor 70-300mm f/4.5-5.6E ED VR lens. She got it as an upgrade from the AF-P DX NIKKOR 70-300mm f/4.5-6.3G ED kit lens that she already had. It is a very good lens IMO.
It has several advantages over the kit lens. It is more robust(should last longer and endure more abuse), sharper, has vibration reduction (this would be important for sports photography) and is an FX mount (meaning it can be used with a full frame camera, if one upgrades down the road). The down side is that it is heavier and more expensive. The 70-300 kit lenses can be had relatively inexpensively. The 70-300mm f/4.5-5.6E ED VR runs a good bit more, but is far less expensive than a larger, longer zoom. Those zooms can be rather heavy and more unwieldy as well. Used on your D3000 crop frame body, a 70-300mm lens will be effectively 105-450mm, which is a fair amount of reach.