...I was told it doesn't autofocus in video...
The 5D3 will autofocus in video, both before and while rolling. However this is single-shot AF, not continuous AF and you must trigger this by pressing the AF-ON button. That single-shot AF can be either contrast detect or phase detect (quick mode, if not rolling).
If done while rolling video, a slight brightness glitch will be recorded, which you'll either have to accept or edit out.
For casual hand-held video, image stabilization is vital. I would strongly suggest you use a 24-105 f/4 or similar lens which gives IS plus a decent zoom range.
You can put the camera in programmed auto and just shoot video. However the shutter speed will not be maintained at 2x the frame rate (1/60th for 30 fps). This may cause strobing effects for moving subjects under some conditions. http://tylerginter.tumblr.com/post/11480534977/180-degree-shutter-learn-it-live-it-love-it
Also in bright conditions the aperture will stop down, so you lose the cinematic shallow depth of field. Maintaining a wide aperture *and* 1/60th shutter speed generally requires a variable ND filter for outdoors. However this is yet another manual item you'd have to control. For pro video work we always shoot fully manual (except sometimes auto ISO), check exposure using zebras and focus using color peaking on an EVF. However that's too much hassle for a vacation video.
You'll have the 5D3 with you, and likely you don't want to take a separate camcorder, and want something better than a cell phone video. Just using full auto will at least get some footage. Make sure you take extra batteries because they are consumed much faster in video mode.
As already stated the build-in mic is limited, even a less expensive hot shoe mic would be better. Using IPB (not All-I) at 1080p/30 or 1080p/25 is probably best. You will likely be displaying it on a 30 or 25 fps viewing device.
I suggest you shoot some test material in various conditions beforehand to get accustomed to how it works.