Good wideangle zoom to go with a Nikon D5200?

I think the crop factor is 1.5?

The perspective I want is roughly 24 - 70mm so with the crop factor that will be about 16 - 46mm… But I would prefer a fairly wide max aperture (not f4.5 - f5.6 more like f2.8 / f3.5) and image stabilized would be good too.

Any suggestions?

Quite simply get the 18-55mm kit lens, or maybe the 18-105mm if thats an option
Once you get the hang of things you will know what exact you are missing

You go to a camera shop near you and try out the lenses you have targeted
But that is only when you outgrow your kit lens

NIKKOR Lenses Simulator
http://imaging.nikon.com/...simulator/

For your D5200, you've got quite a price range for what you want.

Nikon makes a fully professional level 17-55mm f/2.8 AF-S lens. Currently, it's my optic of choice for portraits and many wide angle situations. It's a sturdy workhorse of a lens, that comes with a premium price tag.
Review: http://www.bythom.com/1755lens.htm

An alternative might be the Tamron 17-50mm f/2.8. They make 4 versions. Two have VC (Vibration Compensation) and two don't. They also come in versions with and without the internal autofocus motor. Your requirements would be filled by this lens, as it has very good optical quality, and at a reasonable price.

Review: http://www.bythom.com/1750lens.htm

Non-VC version.http://www.amazon.com/Tamron-17-50mm-Di-II-Aspherical-Digital/dp/B00156OZ68/

VC version.http://www.amazon.com/Tamron-17-50mm-Vibration-Compensation-Digital/dp/B002LVUIXU/

I have both the Tamron (non vc) and the Nikon. The Nikon is sharper, heavier, and I never leave the house without it. Before I got the Nikon, I lived daily with the Tamron, because of it's image quality and small size.

Either would be a great choice.