I have a D40, the model that the D3000 replaced. You'll be very happy with it.
I would recommend an external flash as one of your first upgrades. Especially if you're going to be taking pictures indoors, bounced flash can't be beat. I recently got the SB-400, it doesn't have all of the bells and whistles that the other ones have, but it does everything I need it to. It's one of those upgrades, that now that I have it, I wonder how I did without it for so long.
Other than that, the best thing you can do is take lots and lots and lots of pictures. Futz around with different settings so you know what they do (you can learn a lot on your own w/o taking a class or anything).
Also when you shoot something, whether it be a flower, snake, person, landscape, etc take a ton of pictures. Often I'll take 15-30 pictures to get one that I'm happy with. You can't rely on the LCD on the camera, often pics will look identical on it, but then you download them and notice differences that make one better than the other.