Most good taps have a center in the drive end as do the Starrett type tap wrenches. I make small 60 degree points from broken hss endmills to put in a drill chuck to manually tap in the mill. Use your chin to put pressure On The quill handle to keep up with the tap movement as you manually turn the tap wrench. Perfectly straight and good feel for small taps. There’s also the spring loaded tap follower, which is a good project. Check out Blondihacks on you tube. She makes a nice one. Prevent callouses under your chin if tapping a lot of holes .
I power tap a lot on my mills. A tapping head is a fantastic add to your mill tooling. I like the tapmatic ones. Kinda pricy though. If you have CNC without rigid tapping a floating tap holder like those from Maritool are the ticket. They also work great for engraving. sharp taps are critical for power tapping or you will break them. I also avoid carbon steel taps, ok for aluminum or brass but that’s about it. Only hss for hand tapping. No carbide or you’ll be sorry. Leave that for the CNC guys.
Use proper lubrication. Tapmagic aluminum for aluminum. Relton Rapid tap or tap magic ep-extra for steel and other metals. I don’t like tap magic pro-tap. It stains everything steel or cast iron !
to the original question, plug taps are fine to start, bottoming taps too if in a machine and sharp and the holes not too deep. Taper are much easier by hand to get straight.