All but the largest drain snakes may be damaged by use on drains larger than 2″. As a rule of thumb, this means you should not use a snake on soil lines (like through a toilet) unless you have verified that it is a heavy-duty snake designed for use on big pipes.
The issue is that a light-duty snake will double over on itself inside pipes 3″ or larger, tying itself into a knot, kinking, and eventually breaking — which could make your drain cleanout project pretty interesting!
You may not need any snake at all, and you should consider other options before turning to the complicated work of operating a long, coiled snake (whether powered or hand-operated).
For a simple toilet clog, consider vigorous use of an appropriate plunger (the trick is to use a toilet plunger for toilets and a sink plunger for sinks, and to operate the plunger so as to pull waste up momentarily, rather than try to push waste through its clog. Push down slowly, pressing out all the air from the plunger bell. Pull up violently in a stroke of 2-4″, just short of pulling the plunger’s bell rim up from the bottom of the toilet. If a few cycles thusly do not suffice, then agitate violently for as much as a minute at a time (basically, until you’re really tired), again focusing on a fast pull-stroke and more measured push stroke. Imagine TP, matted balls of slimy hair, and that other stuff getting jerked back and forth by your pull-stroke and gravity, and broken up into smaller bits that can rearrange themselves to better fit through the pipe.
Usually, when you agitate the waste and get it pulled sufficiently back off the point of clogging, it will rearrange itself as it flows back down, flowing past the clog and drawing fluid that was trapped behind to wash out the clog completely. Since the solids are flowing into pipes of increasing diameter and with better venting systems and generally fewer bends, they are unlikely to cause another clog further down the line.
If plunging has failed to clear a toilet clog, turn next to a ~6′ toilet snake (technically, a variety of closet auger). The rigid handle and heavy-duty snake size were designed specifically for toilet clogs, reaching several feet into the plumbing waste pipes, usually past the ‘ideal bend’ of a typical bathroom, where the toilet, vanity sink, and tub/shower drain pipes all meet the main soil stack, and where many clogs occur. You’ll want a 5 gal. bucket and garbage bag or other plastic sheeting handy to grapple the soiled tool outside where it can be rinsed before returning. Still, in the end you’re likely to stay cleaner operating the toilet snake than you are trying to operate a hand- or powered snake from a longer coil. Either way, just remember that soap and warm water are your friend.