One of the skills that many primitive skills school spend a good bit of time teaching is fire starting. I've mentioned before how I am hoping to learn friction fire at Medicine Bow this year to add to my skills - never tried it and really am not sure just where to start. Truth be told, my actual fire starting method generally leans to the lazy rather than the skillful. I gather up small twigs first and a collection of medium sizes sticks off to the side. I build a tepee shape structure using the small sticks, toss in a trioxane bar and light it up, adding the medium sticks and then larger as the fire grows. It works reliably (except that one time while I was dating my wife years ago and was naturally trying to impress her with my outdoor abilities), but it really is the brute force method. Trioxane evens burns when wet, so you have to be trying pretty hard to keep it from lighting dry wood on fire. A single tablet burns long enough to boil a cup of water, and I've used it by itself to heat up food without building a fire at all.
But Trioxane is another supply you have to keep stocked and on hand if that is going to be your fire building method. For the sake of versatility, it is good to have in your back up plan some additional man-made tinders that you've worked with before. It's actually amazing wandering around your house the number of things that will burn, and burn well. Some of them are too hazardous, bulky, or inconvenient to carry around in a survival kit or while backpacking, but some of them seem almost made for the task.
Below are a few of the materials you probably have on hand that I've used before and found to be good, lightweight fire starting tinders. In fact, all five of these in the pic below were lit using my cheap Harbor Freight magnesium firesteel easily enough that four of the five were all lit and burning at once.
Now, Trioxane is still my favorite because of how long and hot it burns, but the cheap or free alternatives surrounding it are also excellent. Of the four other shown above, I'd rank them in order of both lighting ease and length of burn: Vaseline cotton ball, steel wool, dryer lint, and then the hand sanitizer gun patch. Oddly, I've noticed a big difference in the brands of hand sanitizers. Some light up and burn a hot, clear-ish blue flame. Some don't want to burn at all. I am guessing it has something to do with alcohol concentration and the lotion additives in some. Also, the steel wool can be somewhat tough to really get going. It doesn't put out a nice visible flame like the others do - focus on getting a good ember started by blowing lots of oxygen on it and it will burn extremely hot for a decent while. Check out the pic below and you'll see what I mean.
There are some great fire starters out there beyond matches and butane lighters. Butane lighters are cheap and pretty durable so they certainly have a place in my fire kit, but they also can break, run out of fuel, or get lost just like any other piece of gear. Having experience using your firesteel or ferro rod is very important, even if it is your back-up method. They're easy to use, but not completely intuitive. Take a few minutes, watch a Youtube video on how to use your specific type, then grab one of the materials above and see if you can get it started using your fire starter. Of course, be careful. If where you are is like where I live, outside conditions have been super dry lately. Take care not to let the lightweight materials like dryer lint fly away from you and spread.