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If there was one thing that could significantly improve your shooting experience without breaking the bank?... I would pick up either the 35mm f/1.8G DX or the 50mm f/1.8G FX for $200.
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This. Though the 18-55 is a surprisingly good lens. Don't worry too much about the gear, spend the time playing with aperture, shutter speed, and ISO. "Bracket" a fixed subject, see the effects of changing speed and light have on the image.
I'm a big fan of tripods; but I take a lot of low-light (and night) outdoor shots. If you get a tripod, don't buy the $20 Wal Mart special. Bite the bullet and get a $120 Manfrotto or similar; doesn't have to be fancy carbon fiber top-line, but you want solidity and stability.
Get a remote. I'm pretty sure the 3300 works with Nikon's ML-L3; a $15-$20 infrared remote. Lets you take self portraits and also lets you take tripod-mounted long-focal-length shots with minimal camera shake.
But the best thing you can do take LOTS of pictures of LOTS of subjects. Digital photography is essentially free, once you have the camera. Bad shots get deleted.