Shop used. and from reputable vendors that will take returns.
Adorama actually has two D610s for $250 rated at G. This is a lower rating for them -- but if they are actually still functional and they just appear to be heavily used -- that's an amazing deal. Great thing about them is if it doesn't work out, you can return it back to them.
They have E and VG rated D600s for $400, but I wouldnt a buy a D600 now unless you call Nikon and see if it's been serviced for the oil issue. Their service advisory on the D600 ends on Jan 10th. So if you could get one and send it to Nikon ASAP, that would still be good -- but really pushing the end of the free service.
Otherwise the D610 is a fantastic camera whos used value is still an insanely good deal, for one of the top 20 rated sensors on the market, today.
The D3xxx series is Nikon's entry-level. Don't be fooled by their lens packages -- you can buy those two lenses
used for $90 and $130 respectively. So that right there tell you how much the camera body itself is worth.
While it has a great crop-sized sensor in it, Nikon dummies down the featureset of the D3xxx model line to the most basic functions in order to keep the "cost down." The D5xxx series is a much better platform -- So long as it has the 24mp sensor.
But I would personally recommend the D7100 or D7200 as they have a more "pro" level body, and a sensor that does well in low-light for its size. Both are also still very decent cameras for day-to-day. And like the D610, and unlike the D3xxx and D5xxx, it can drive D model Nikon lenses.
The D300 recommended above is simply too old. It was great at it's time, but simply a relic today and wasn't designed for what you need. The D700 would be a better choice, which has a better full-frame sensor, and I would still discourage it for the same reasons. (early 2000s tech, dont focus well in dark, low resolution, bad ISO/DR, etc).
I don't like the 5DmII recommend either, google ISO invariance. The 5dmII has horrid ISO invariance, Canon didn't solve this issue until the 5DmIV -- not what you want when shooting the night.
If you want to capture the northern lights in Alaska, you need a camera sensor that works well for night and long-exposure work and a lens that can do the same. The biggest problem you'll find is your budget -- the used camera market artificially keeps value high on junk old equipment, and lenses retain value as they pretty much last a lifetime.
This is just my opinion, but I'd personally rather have a decent/better/capable camera body as a base and work from there without the need/desire to upgrade later. Most your money will go into your lens investment.