Ok, a question I feel qualified to answer! Background,, I worked for 15 years or so on motorcycles, repaired countless tires. Later worked at and managed a tire shop where we did tires from wheelbarrows to backhoes. I have patched/plugged/replaced literally thousands of tires. Best way to repair a tire is to do it from the inside with a patch. Big reason is from the outside you have no way of knowing what the damage is. I have seem a simple nail, from the outside, be an inch and a half break in the cords on the inside. When a tire is run low of air it will overheat. Over heating will cause the rubber and plys to come apart, not readily seen from the outside. When plugging you assume you are following the original hole, often you are not. Plus a 1/32 nail becomes a 1/4 inch hole to allow for the plug. Also when looking inside a tire it is common to find other nails, screws, damage other than what you first thought. We used to be able to get patches with cords in them that would work on sidewalls, both bias ply and radial patches. Having said all that, plugs work. I prefer the rubber, arrow shaped ones that are shot in with a caulking gun type tool. But the snotty yarn type work also. Any of the stop leak/slime type stuff can work, but I have seen them loosen old patches and plugs, rust wheels and in general are a real pain in the butt for the poor guy that has to change the tire. I even saw where a guy used canned milk in a tire, when it curdled, it worked very well. But when I changed the tire it smelled like it was filled with baby poo. I did my best imitation of a cat gagging on a hair ball for an hour. Bottom line, plugs will work, often well into the sidewall. But without knowing how much damage is on the inside, it can be a crap shoot. I carry plugs in my work truck. Common on construction sites to get nails and a quick repair is a time and money saver when it works. One thing on a 30mph minibike, another on a 80mph street vehicle. Proceed with caution!
Sometimes you need to patch the inside of tire before you install a tube. The original hole, if rough enough, can eat a hole in the tube. Sometimes just buffing the ruff spot works. Dragging a rag around the inside of a tire helps as it hooks on small nails, burrs, cactus thorns that can be hard to see. A shake of baby powder between tube and tire helps keep the tube from sticking to the tire and tearing.