I am new to dslr's and got a nikon 3000 with 18-55 lens as a gift. I already see some limitations with the lens for walking about or on trails. So my question is being new should I go with a 55-200 or 55-300 or is there another step before I go with a telephoto lens.
A 200mm lens is pretty long on an APS-C DSLR, equivalent in length to a 300mm lens on a traditional 35mm (or "full format" DSLR) camera. Of course, you may still find that length limiting for some purposes, but it's more than adequate for most genres of photography. And new or used, the 55-200mm zoom (with or without VR image stabilization) is a cheap lens that will let you explore your direction in photography without a major financial outlay.
Perhaps the most important thing when buying photographic equipment is knowing what you really need. Lenses, especially, can become really expensive in a hurry. By exploring the cheap option now, you will be in a better position to decide, when the time comes, whether you need, say, a good, fast, long lens (zoom or prime), or something with the ultimate in versatility (like, say, the 18-200mm zoom). The relatively low price of the 55-200mm will give you the full range of focal lengths, and you can tell by the kinds of pictures you find yourself taking (or still wishing you could take) what your next step should be. If all or most of your pictures are at longer focal lengths, then a faster 70- or 80-200mm zoom might be the ticket. If you find that you're working consistently between 55 and 100mm, then you might find that a shorter zoom or an 85mm prime lens is really what you need. Or you may find that having the "dual kit" is perfectly adequate for your needs.
If the 55-200mm doesn't do the trick for you, you can sell it for nearly what you paid for it. If you splurge on something that doesn't scratch your immediate itch (wanting a longer reach), you may find yourself with something you'll take a significant loss on when you change your mind. Don't worry about what's "right"; take the time to figure out what's right for you. When you're ready to jump into the deep end, you'll know.
This question is very subjective. With the limited information provided, I would suggest to someone after the kit lens to purchase a 50mm f/1.8 lens, followed then by a 70-200mm telephoto. That is, if they really are having trouble deciding on their own, and are unsure of what type of photography they want to shoot.
With a Nikon DSLR, the simple answer to your question would be to get the 35mm F1.8 Nikkor. It is an essential piece of glass, light and fun to use providing an excellent range for all types of shots especially in low light and indoor. Things that a kit lens does very badly. When I bought my D90 I dropped the kit lens for the body only and added the above prime. I have a range of lenses now but that is still the favourite after 2 years and 25,000 worth of photos.
I'd add my $.02 that the "next" lens after the kit lens should -- very possibly -- be a replacement for the kit lens. Many kit lenses are relatively low quality, great for showing you that your camera works right out of the box. But really, shouldn't you be looking for a good general purpose lens before looking into a telephoto? Something that spans moderate wide angle to moderate telephoto?
In the Canon world, this might be either a 24-70mm or 24-105mm zoom. There are days when I'm tired and this one lens is just enough. Other day, I carry a bunch of lenses, but it's good to know that I have a high quality zoom lens that will act as a wide angle, normal, and telephoto.
Agree with @dpollitt that the question could be refined to make the answers address specific concerns.
Although you don't specify what exactly you want to do with the lens, I would suggest a 50mm fixed focal length lens, or, considering that you are using a D3000, a 35mm fixed lens - giving you approximately a 50mm lens equivalent.
If you mean to replace it with another zoom, then the 24-70 2.8 is a great bit of glass. Or if you want longer, then as mentioned above, a 70-200 won't disappoint.