Tips for plane spotting equipment?

So for promotion I'm getting a new camera (most likely a Nikon D3300) and I'd like to know what kind of equipment I'll need when plane spotting. This includes lenses, lens hood, all those other items. I love my current camera but when I'm plane spotting at sunset my shots get ruined by noise and tend to take longer to autofocus. This being said, it would be nice to get a camera that is capable of doing long exposures and taking good night shots. Also, me being an amateur photographer, I'd like to know how I'd be able to take good nightshots with the future camera. Also I appreciate any thoughts on whether this camera is good enough for plane spotting. Also I would draw the budget line at about $600-700.

If you are shooting in full sun, the Nikkor AF-S 70-300 mm VR will do the job and the lens is well within your budget of $600 to $700 ($590) for the lens

I hope you are aware that using long exposures of aircraft landing will show a blurred image unless you pan with the aircraft and let the background blur, showing motion.

I would suggest one with good quality and fast capturing skills. I have a Canon and it's great. So you can choose but I recommend the qualities above

I'd go with Canon's T5i or T6i over the D3xxx series by Nikon only because the Canons shoot 14-bit RAW that have 4x greater tonality than the 12-bit RAW files from the Nikon D3xxx. This means you get more tonality, much more data in the shadows and highlights so you will have a greater amount of adjustability in post.
Nikon's D5xxx and higher all shoot 14-bit files and amazing dynamic range.
All of this means that you must shoot RAW, otherwise you'll end up getting 8-bit JPEGs. Each 'bit' doubles the tonality that the file can hold. Eight bits (2^8) has 256 tones, 12-bit has around 4,000 tones, and 14 bits has around 16,000 tones. A single bit is a huge deal.

Shooting moving subjects (airplanes) at sunset and in low light is a challenge for any camera, and photographer. The D3300 will be as good as any camera in your price range but there will definitely be a learning curve to getting great photos in less-than-ideal conditions.

I suggest you hang out in one of the several airplane enthusiast forums and get tips from the experienced members there. Some, like the following, have sections devoted to aircraft photography:
http://www.airliners.net/aviation-forums/aviation_photography/