Light trails of cars at night you actually want a long exposure, so a large aperture lens isn't needed. You'll definitely need a good tripod though, along with some sort of remote release to trigger the camera. I use the ML-L3 wireless which is like $15 USD. For night time photos of things that don't move (scenic) you'll either need VR, a large aperture lens, a tripod, or you can forget all that and just use some of the good ol fashioned handholding techniques.
I pulled
this off at 1/8s and iso1600 with my 18-55 at f/3.5, and that's a 2.5EV shot which is pretty dark. I also had absolutely nothing to brace myself against and was free standing with some gusts of wind. With a wall or something to brace against or even sitting I could have pulled off a 1/4s (iso800) or even a 1/2s (iso400) shot which would have been cleaner. The limit for any sort of handholding is usually about 1s, unless you're passed out and drunk like a friend of mine who once rested his camera on his chest pointing up and did a great 15s exposure of the stars.
The best thing to do is to just take a few photos and then pick the sharpest and most blur free on. For that Louvre shot in Paris, I took a burst of three photos, and luckily one of them was sharp and blur free, even at that slow shutter speed.
For indoor club/event people photos where it's dark, you can't use the long exposure since people will never hold still that long. Either you need a really fast lens, or just use a flash. f/2.8 is still way too slow. A 50mm f/1.4 for around $200 used or $300 new might be a good investment. You'll probably need to practice a lot because there's very little depth of field at f/1.4 so you'll need to focus very precisely, usually on people's eyes. 50mm also might not work very well for group shots. There's the 28mm f/1.4, but that puppy is over a grand used and not even made anymore. It's considered a collector's item now.
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