If your main purpose is shooting video, I'd probably steer you towards something that was actually designed to shoot video rather than a still camera that just has video functionality grafted on as an afterthought (as all DSLRs do, IMO). Don't get me wrong, you can certainly shoot movies with a DSLR, but IMO that's like buying a Toyota SUV to tow the space shuttle. It can sort of do the job under the right circumstances, but it isn't really the right tool for the job.
You can probably find a used XH-A1 or even an XH-A1S in that price range. They have image stabilization that actually works well for video purposes (unlike DSLRs). They have dual XLR audio inputs with phantom power (as opposed to an unbalanced 1/8" connection with no phantom power like DSLRs have), a switchable ND filter, manual control over pretty much everything, zebra stripes to quickly spot overexposed areas, etc. They're designed to be a "grab it and forget it" all-in-one ENG/EFP package, and they do that job well.
About the only thing the XH series doesn't have is a removable lens, but the superzoom it comes with is reasonably solid, IMO. It has a 35mm photographic equivalent range of 32.5mm - 650mm (and that's before you kick in the digital zoom) at f/1.6 to f/9.5, depending on zoom setting. You probably won't want to use it at its widest setting too often because of the barrel distortion, but that clears up nicely by about 6mm (equivalent to a 43.2mm FOV on a full-frame camera).
If you can manage to save up a little more money, I've seen used XL-H1A camcorders for somewhere in the neighborhood of $2,500. That's the removable-lens version of the XH-A1. In addition to supporting special-purpose XL-series lenses designed for the XL series of camcorder, it also can be adapted (officially) to use EF lenses (with a whopping 7.2x crop factor).
