Your best bet will always be to pre-select a single AF point and work to keep that on target. If you can do that, you'll eliminate chances that the camera will choose point of focus incorrectly. If shooting fast, you may not have time to change the selected point, might have to stick with center one only. If that ends up making images overly centered, try shooting a little more loosely (zoom out slightly) to allow some room to crop in post-processing.
Zone Focus is probably your second best choice most of the time. It can be better than Single Point when you have trouble keeping AF points right on the subject, but works best when there are a lot of distracting objects behind or around or in front of your subject. For example, it can work pretty well focusing on a bird in flight against a plain sky, but might not work as well for a bird flying through trees.
All Points leaves a lot up to the camera to decide. You might have good luck with it in some situations, but not in others. I rarely use it on any Canon... just don't like to leave it up to luck that the camera will focus where I want it to.
70D doesn't have the 7D's Spot Focus (smaller AF point for higher precision, but a little slower focusing) or Expansion Points (similar to Zone Focus).
All 19 AF points on both 7D and 70D are the more sensitive "cross type", but (like nearly all Canon cameras) the center one is further enhanced when used with f2.8 or faster lenses.
There are a number of fine tuning adjustments you can make to the AF system, nicely grouped together in the menu under Custom Function II, Autofocus. The most important of these might be Cf.N II - 1, Tracking Sensitivity. First inclination might be to dial this up... but that would be a mistake. This doesn't actually change the speed of focusing or the camera's tracking capabilities. Instead it sets how quickly the camera jumps to another target, such as when an obstruction temporarily passes between you and the subject. Most people benefit from turning this down a notch or two, at least until they are more familiar with the camera (or better at avoiding obstacles with Back Button Focusing, see below). You might find you can turn this adjustment back up, after some practice with the camera and settling into, becoming accustomed to some of the other AF methods you'll be using.
C.Fn II - 2, Acceleration/Deceleration Tracking is new on 70D, not available on 7D. It is most likely useful with subjects that change speed and/or direction (which C.Fn II - 1 set to "slower" might make more difficult). Experiment with it and moving subjects. Essentially, C.Fn II - 1 and C.Fn II - 2 divide one of the 7D's C.Fn into two separate C.Fn's on 70D.
C.Fn II - 3, First Image Priority - I'd probably set to Focus Priority, since images that miss focus are of little use to me, even if it slows down shooting a little. I'm not sure, but this might also be useful for "trap focus" techniques.
C.Fn II - 4, 2nd Image Priority - Probably should be read as "2nd and all subsequent images in a burst". Again, I'd probably set it to Focus Priority, since I can live with slightly slower burst speeds, if it allows for more accurate focus. C.Fn II - 3 and C.Fn II - 4 are another example where 70D has two separate custom fucnions that were combined in a single C.Fn on 7D. I'm glad to see Canon doing this.
Most of the other Autofocus related C.Fn's are more minor tweaks, in my opinion. Except possibly for C.Fn II - 9, Orientation Linked AF Point Selection. I experimented with this on my 7Ds and found it seemed to slow thing a little, so I turned it off. I'll be interest to see if it works better on 70D. It's a neat idea, that you can have different AF points selected depending upon how the camera is oriented. If you experiment with it, it's important to rememeber that there are three orientations to set up: horizontal/lanscape camera orientation, vertical/portrait orienatation with the grip at the top, and vertical/portrait orientation with the grip at the bottom. You have to be sure to set up all three, or in the heat of shooting you'll somtimes find yourself wondering what the hell just happened (don't ask me how I know :rolleyes. Oh, and you also can set up different focus methods for different orientations, such as Zone for one and Single Point for another and All Points for the third orienatation.
C.Fn II - 11, AF Point Display During Focus I would likely leave set to the default (0) except maybe in special circumstances. This allows the "smart" focus screen to do its thing, displaying only the active AF point(s). I can't think of any time I'd want the camera to display all points, all the time (1). That sort of defeats one of the key abilities of the transmissive LCD focus screen. Two of the other arrangements may have some uses in certain situations... I'd have to study and experiment with (2) and (3). I can't image why I'd want to turn off all AF point indications (4), any more than I'd want them all displayed all the time.
C.Fn II - 12, VF Display Illumination I set to "enabled". This flashes red when AF starts, and in One Shot will flash red when focus is achieved and locked (but not in AI Servo, since AF never locks in that focus mode). Unlike cameras with the "dumb" focus screens, this flashes the entire display in red (all AF points that are showing and the grid, if you have it enabled). It doesn't flash only the one, active AF point. It might be a little distracting in some situations, but you can get used to it. I hardly notice it anymore.
I'd suggest don't mess with C.Fn II - 13, AF Microadjustment until you are sure some of your lenses are off and need it. Be sure to read the instructions carefully and search here on POTN for methods and tricks to MFA... It is the new, improved version on 70D (up to 40 lenses, two points of adjustments on zooms, and it's lens specific by serial number). You might never need it, unless you shoot big aperture lenses wide open a lot.
With moving subjects in particular, you may want to experiment with Back Button Focusing. (Actually it can be used with all types of subjects, tho BBF is especially helpful in AI Servo, when tracking and photographing moving targets.) If you wish to set this up, you'll need to go into the menu, Custom Function III, Operation/Others and select Custom Controls. Then navigate to the shutter release button icon, and set it to Meter Start only (in other words, disable AF Start at this button). The camera will now only start AF when you press the AF On button with your thumb. Optionally, you can swap the functions of the AF On and * buttons. I do this because I prefer to use the larger, more prominent * button for focusing, and the AF On button for less frequently used AE Lock (that's normally assigned to the * button). It takes a little practice, but for most people BBF soon becomes second nature and many wonder why they would ever use anything else.