If you want simple, I'd stay away from DSLRs. Most won't have continuous autofocus (the Canon 70D is the exception) that is effective.
Go with a camcorder. A higher end consumer/prosumer camcorder would be ideal and aside from possibly having white balance (point at a white sheet of paper and press a button), it's pretty much ready to go with nothing to adjust.
I'd avoid the Sony VG20 right now. The kit lens is junk and there's no reason to spend the money on an interchangable lens camcorder when they have better camcorders for half the money.
Here are a few to take a look at:
Sony HDR-CX900
Sony FDR-AX100-it's basically a CX900 with 4k capability at the cost of an extra $500
Sony HXR-NX30U-this one is based on an older design with the best available image stabilization on the market. $1600 after a $200 rebate and includes a full version of Sony Vegas Pro 12 if you need the software. Also includes a XLR microphone rig that is $800 by itself.
Canon Vixia HF-G30-solid and very easy to use camera. Also comes with a full version of Sony Vegas Pro 12.
Canon Vixia XA10-based on the older HF-G10 camcorder with the addition of XLR audio (you need to provide your own mic)
If you want low cost and have a best buy around you, you should look into the
Canon Vixia HF-G20. They should be on clearance, bringing the price down to the $600-700 range. Two stores near me have it priced at $599.
For mics, if you think you'll have trouble remembering to turn on the mic, most camcorders have optional mics made specifically for a particular brand/hot shoe that are powered from the camcorder so they turn on automatically when the camcorder is on. If you want a universal solution, I'd recommend looking into a
Rode Videomic (the one with the Rycote Mount), the
Shure VP-83, or the
Sennheiser MKE 400. I have all three of them and prefer the Shure, but the Sennheiser is great if you need something small.