I avoid HSS taps at all costs. If you break one, you ain't gettin' it out easy. If a good plain high carbon tap breaks, you can use a punch and bust it out, and usually, you don't even damage the threads you have already cut. Sometimes, though, HSS is all you can find. Use them and be careful. I tried the Brownell's tap extractors years ago (the little finger deal). Not worth fooling with. If a tap is broken, it's probably because it's stuck (usually because it was dull), and them little fingers ain't gonna turn it out.
I like Hanson taps. I hate Vermont American taps. They suck badly.
You know that it's time to replace a dull tap when it just don't cut well anymore. A dull tap is dangerous, and an invitation to breakage. It will get tight, feel "squeaky", no matter how well lubricated, and they're easy to snap off when they get like this.
I often tap just by hand. Yes, you can get it cocked. The longer/deeper the hole I guess the straighter you could get the threads going by hand. I have a pretty good eye, and don't have too much problem getting crooked threads, though on more critical screws like bridle, sear, frizzen screws, etc. I use the drill press gizmo, which is made to go into the drill press and holds the tap vertical, and I use that to tap, or at least start tapping (It's not driven by the drill, it's just held in place and you turn it with your hands). After I get it going, I will usually finish by hand, as I can keep it straight and I can feel what it's doing. You gotta be able to feel it.
Although people will scream, I just use motor oil to lubricate. It works fine. Do about a turn or so, then back up a bit to knock the chips out. Turn again and back up. Turn again and back up. Blow the chips out every now and then, and if necessary, just take the tap out and clean it out and then put it back in to finish.
Unless you drill blind holes, you'll never need a plug or bottoming tap. Sometimes you need to drill blind holes, though. I will often take a broken tap or a store-bought bottoming tap and carefully grind the tip down to make a truly bottoming tap for doing that last little bit.