"variety of settings; interviews, sports, outdoors, indoors"
means a few things... look to those who do similar work, i.e., electronic news gathering (ENG).
The camcorders used have large lens diameter and imaging chip system. The large lens diameter allows light in for processing, the imaging chip system (3CCD or 3CMOS) processes the light. Because they are large, their lighting "window of opportunity" is much larger than those with smaller lenses and imaging chip systems.
I agree with terfyn that audio input and headphone jacks are important.
As far as I know, camcorders under about $8,000 come with a built-in fixed lens. Add-on lenses are available, but not required. The exception to this is the Sony NEX-VG series. There is no equivalent Canon camcorder in the $ range you state that uses an interchangeable lens system like the Sony NEX-VG series.
If you are considering a dSLR to capture video (hence your reference to "a bunch of lenses"), be advised that while they can capture great video, they are not designed to be used as a camcorder. Reading through the manual of most dSLRs capable of capturing video, there are warnings about file length limitations and overheating during prolonged video capture times. Neither of these are issues with camcorders. And referencing the fist line in this reply, very few ENG users use a dSLR to capture video. You probably don't need a big shoulder mount camera - but something in-between... and more likely camcorder rather than dSLR.
As well, if your plan is to use the video capture device to also capture the audio for the final product, I am not aware of any dSLR with manual audio gain controls on the outside of the camera. But on the higher end (i.e., prosumer) range of consumer camcorders, this is common. For external audio gain control on a dSLR, that means adding an XLR adapter (juicedLink and Beachtek among a few others).
All image capture devices can do a great job when used within their design parameters. The manufacturers don't do a very good job at identifying the difference between a $200 consumer camcorder, $1,000 dSLR or $2,000+ camcorder... reading their marketing material, one gets the impression that all cameras behave equally well under all environmental and use conditions. This just not the case.
Don't get me wrong - dSLRs can capture great video when that secondary "convenience feature" is used properly. I am merely saying they cannot be used as a replacement for a camcorder that can record video for as long as there is power and storage available.
We don't know if your budget includes lighting, mics, external audio recorder, tripod or other steadying devices, optional high capacity batteries from the camcorder manufacturer, cases, computer hardware/software upgrade to edit the captured video, and lot more... Once we know what your budget includes, we can start making recommendations.