I used the Sigma 70-300 and kit combo for years before I felt the need to upgrade. They are available used for $100 or less. One advantage to the Sigma is the 1:2 macro, which is actually often useful long after you upgrade to better glass. It's also an excellent lens from 70 to 150, although it gets a little weak in the long end, but all that type of lens does. At 90mm it's images are only a little less in IQ than the best available.
With the kit and the 70-300, there isn't much you can't cover. I've taken mine in twice to trade in and haven't been able to let go of it. And in some situations, it's still my lens of choice. Those situations would be
1. Good light (it's doesn't open very wide, 6.3 @ 300 for example)
2. Subject not to far away over 150mm. An image at a distance will not be captured accurately. (It will look like someone ran it through a Photoshop Watercolour filter.)
But for close ups , and from 70mm to 150mm it's a great lens. You're not going to do better for $100. I've seen them on kijiji for $70. The below image was shot at 150mm and F 5.6, both settings really play to the lens' strength.