O.K, well before spending any money you need to have a think about what it is you want to shoot. If you're going to be doing a lot of landscapes, the 70-300 will be fairly useless to you. If however you want to shoot small things from far away, like wildlife, birds, motorsport, then it's a very good starting point. If you want to shoot very small things (insects, very close up views of flowers etc) then my recommendation would be something totally different!
My advice for the time being would be stick with the kit lens. Use manual/aperture/shutter priority, and shoot everything you feel like shooting. Eventually you'll get a feel of what it is that's letting your current setup down, be it reach, no macro capability, too small a maximum aperture, or something else. Have an experiment, and see what you can come up with!
Chris