Well, DX lenses do fit on the FX bodies, at a reduced view and resolution. Ideally, you want to avoid them, but unlike Canon, the "wrong" lenses work fine. I use a 10.5mm f/2.8 DX fisheye on the D3 a lot. It was was bought for the D200 in mind, but buying yet another fisheye, when it's a lens I rarely use, would be stupid. (At least, in my budget, and I understand yours is the same or lower than mine.)
Each manufacturer makes up their own brand name for various lens aspects, be it stabilization, crop factor, or whatever else. I find the easiest way to avoid confusion on these items is to visit the manufacturer's websites, and just reading what their non-sense brand names actually mean.
Sigma, for example, uses "DG" to mean "digitally optimized". That's just a fancy way of saying the lens elements have coatings (usually on both sides of glass, maybe even dark matting of the barrel itself) that prevent the ugly glares, ghosts and other artifacts that are easily picked up by digital sensors -- especially modern high-resolution ones.
The rules of optics still apply. In general, Canon and Nikonr make the best glass for their respective cameras. There are sometimes lenses by third parties that are just as good or almost as good (example: Sigma 70-200 f/2.8), or maybe even lenses that are BETTER -- yes, better! -- than the Nikon/Canon ones (example: Tokina 12-24 f/4), although this is far less common.
I've looked at the Sigma 24-70 f/2.8 myself. If I needed a lens in that range, I'd probably have to buy it. I'd want the Nikkor, but not for ~$1500 USD.
Side note -- I don't really need that lens, I find myself using a 12-24, 80-200, or the fixed 50mm. In these economics times, I'd just assume keep $500 saved aside, rather than buy a lens that might get pulled from the bag once a month -- and it's not like I can't operate in that range in a pinch, as I've got an older 28-105 Tamron as well as the Nikkor 18-200. The Tamron is not "digitally optimized", and it has artifacts at f/4 and below. The 18-200 is only 6MP on the crop, in a D3/D700 sensor (not a bad MP, just not "full" use of the camera). Sometimes it's good to ask yourself "do I really need this exact lens, or can I make due with something else that I alreay own?"
The only cropped lenses made by Nikon are clearly marked "DX", yes, At least to my knowledge. I'm not aware of any oddball "early" lenses that did not have "DX" stamped on them. In those early days, in fact, on a D1, we were still mostly "stuck" with our film lenses. Many of us still shot our F4's/F5's too, at the time.
The only other lens I've considered is the Nikon 28-85 f/2.8-4 lens. It's "pre-digital" but I see no complaints from owners. It's worth looking into, if you can find one local to test out.
On that Sigma, I've read a lot of reports where sometimes the exact lens is bad in some way. They do produce lemons. I ran into a similar problem with that 28-80 Tokina I purchased last year. Great lens for most folks, mine was a dud. So only buy it in-person, don't buy it online or without being able to test it extensively on your own body. I found a Tamron dud last year, had my laptop in the car. I shot in the store, went outside, and processed the images. The lens was just pitiful. Test shots from it (and others) will end up on the photo expansion area of this site, when discussing a yet-undetermined related topic, sometime this year.
Personally, I save my money, buy fewer lenses, and make sure they're all Nikkor. I made an exception for the 12-24 Tokina, and its been excellent. My older Tamron was a film-aged lens, it doesn't count, as it was great for many years. The other "bad" Tokina was a mistake that cost me $500 in 2008. Don't learn this lesson the hard way like I did.
What's the point of buying a top-of-the-line camera if you stick crap glass in front of that costly sensor? Same goes for cheap filters in front of good glass. It's good logic. I have to remember this myself, resist the urge to cut corners.
As always, I'll answer your questions as best I can, if you need more help. You may or may not run into questions when trying to decipher lens branding nonsense. Just post ones that are confusing, preferably with links to the manufacturer site, for the lens or term in question.
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