Neutral really is the best setting (unless you're shooting b camera and your a camera is in log mode in which case you can use cinegamma, but that's a rare situation to be in so don't sweat it!) because of the lack of sharpening (which is poorly implemented) and the color balance is best in neutral; faithful has a bad tint and the rest are all exaggerated and unnatural. The amount of contrast and saturation are your call based on what look you want. I keep sharpening at zero but the footage is very soft with this setting; it's still preferable to the halos you get with sharpening, though. Keep highlight tone priority off to reduce noise in the shadows; keep it on if you have blown highlights (I keep it on always).
This is the best book for video production by far:http://www.amazon.com/Bare-Bones-Camera-Course-Video/dp/0960371818
It's more for old video and film, but it will give you the idea and you can read it in an hour or two, not that you'll want to because it's surprisingly technical and dense for a beginner's book.
The best single lens would be a 24-70mm f2.8 zoom, imo, but your kit is very appropriate for video. In general, a set of cinema lenses consists of an 18mm, 25mm, 35mm, 50mm, and 85mm but on the 5D you can multiply those by 1.6X to get the same FOV as super35 and that would be a normal range of focal lengths, 28-135mm (but a 24-105mm zoom will do it, too). But everyone has different taste. In my experience, most day exteriors are shot at f4-f5.6, most day interiors at f4, most night interiors at f2.8 and most night exteriors at f2 or thereabouts. But this varies...David Fincher has recently shot everything wide open and you will see some other movies with very deep focus, obviously, but this is a good starting point, imo. Use 1/50 shutter (or 1/60 if your source flickers) and ND filters to control your stop. By a full kit at 77mm: .3, .6, .9, 1.2, etc. and a polarizer or a variable ND if you don't care about color shifts and step up rings to 77mm for all your lenses with smaller threads. But the 5D has a bigger sensor than cinema cameras so you can stop down a stop more to get the same depth of field.
Good lighting and camera support (tripod, dolly) will help. Renting is cheap, too, if you ever need other gear. The 5DIII isn't great but it's very good for video for the price. You can do anything with it and a few good lights and lenses.