There are really only a few key things you need to keep in mind, regarding shutter speeds...
Essentially the rule of thumb with full frame/film cameras was that the shutter speed needs to be the reciprocal of the lens focal length, in order to hanhold a steady shot and minimize camera shake that causes blurred photos. For example, most people could successfully handhold a 30mm lens at 1/30 shutter speed... a 100mm lens at 1/100... a 200mm lens at 1/200, etc.
However, both your cameras are "crop sensor", APS-C, which is smaller than FF/film and sort of magnifies the image.... and magnifies the potential for camera shake blur. Multiply your lens focal lengths by 1.6X for a more appropriate shutter speed to use with those cameras. So, for example, that 30mm lens on your camera would need 1/48 shutter speed, the 100mm lens would need 1/160 and the 200mm lens calls for 1/320. (Obviously not all these exact shutter speeds are available... so use the next faster one... such as 1/50 or 1/60 instead of 1/48.)
Slower shutter speeds can be used... but maybe not handheld. You may need a monopod or tripod to help hold your shot steady.
The above shutter speed guideline doesn't take into accound Image Stabilization, which several of your lenses have and which helps steady your shots, too. Often the effectiveness of IS is estimated in "stops"... "two to three stops assistance" is fairly typical. For example, this means a focal length that you'd want to use 1/60 shutter speed with, in the absence of IS ... When you have IS you probably will be able to handhold at 1/15 (two stops slower) or even 1/8 (three stops slower) shutter speed.
All the above is estimates because people are different. Some of us are able to handhold steady shots at slower shutter speeds. Others have shakier hands and need to use faster shutter speeds. So you need to learn what works for you.
With moving subjects, you have to decide whether you want to fully freeze the movement or if you want some subject blur in your images and, if so, how much. The speed and direction of the subject makes a difference how high shutter speed is needed to fully freeze it. The same is true the other direction... subject speed and direction also effect how slow a speed is needed to introduce the amount of motion blur you want in your images.
I'd suggest you practice shooting moving subjects, experimenting with faster and slower subjects, subjects moving toward or away from you as well as those going past you on the perpendicular, and with different shutter speeds to get a feel for how you can control the results in your images. I don't think a tutorial or blog post can give you a real feel for these things. That you'll have to develop with hands-on experience and practice.
A third type of image blur is another type of camera shake, due to internal vibrations from "mirror slap", which only occurs within a certain range of shutter speeds. It varies, depending upon the size and weight of the camera's mirror and other moving parts, but basically there is some risk of it around 1/30 and slower to about 2 seconds. It's usually not an issue with faster or slower shutter speeds, and on cameras like yours with smaller size mirror and shutter, might actually only be 1/15 to 1 second or less. Other cameras with much larger mirrors (such as Pentax 6x7, which has a mirror approx. 12X as large as the one in your cameras) may have a wider range such as 1/60 to 4 seconds, at risk of shutter shake blur from "mirror slap"
Just be aware that when you need to use shutter speeds in this particular range, it can help make for a steadier shot if MIrror Lockup (MLU) is used. On most modern Canon, Live View can serve the same purpose. This lifts the mirror out of the way well in advance of taking the shot, so that any internal vibrations can subside before the image is made.
It also can be a good idea at shutter speeds 1/30 and slower to either use a remote release so that you don't cause any vibrations when you press the shutter release button of the camera. Alternatively, the self-timer delay can be used for the same purpose.
Another situation where shutter speeds have some limitations is when using flash. Your cameras have a flash sync speed, which is the highest "native" shutter speed at which the flash can cover the entire image area before the shutter closing would partially obscure it. It's probably 1/200 on your T3i and 1/250 on your 70D. You can use these speeds or slower with portable flash, without much concern. (Note: studio strobes often require slower sync speeds, probably 1/125 and 1/160 with your cameras.)
Now, most Canon flash and some others have High Speed Sync mode, which is where the flash fires a shorter duration burst that's carefully timed to match higher shutter speeds. With this you can use flash at 1/500, 1/1000 or even the fastest 1/4000 and 1/8000 shutter speeds on your cameras. However, using HSS seriously reduces the distance the flash is able to reach. The higher the shutter speed, the less reach.
Finally, shutter speed is closely inter-related with aperture and ISO... or, in other words, with controlling depth of field and/or image qualities such as resolution and noise levels. Rather than try to get into the weeds about these here, if you haven't already done so, I highly recommend you pick up, read and study a copy of Bryan Peterson's "Understanding Exposure". This is an excellent book for both new shooters and more experienced ones, from the basics to more advanced info about the exposure triangle - shutter speed, lens aperture and ISO - and all it's nuances. Get a copy of "Understanding Exposure"... it might be the best $18 you ever spend on your photography!
I see someone else has linked to "Cambridge in Colour" website and they do have some very good online information there. Another excellent site with tons of photography-related info is Luminous-landscape.com
Hope this helps.