The drum throne just may have the highest ratio of most-critical/most-overlooked in terms of components of the kit. That's mainly because of the simplicity of its function. Hey, it's a seat. You sit on it, and that's it. What's the big deal?
Here's the big deal. If you're going to play with solid, steady time and provide a strong foundation for the band, you need to have a strong foundation for yourself as well. This is to say that your physical foundation needs to be rooted and connected to the ground, like the roots of a great tree. Yet all too often I see drummers playing on seats that are unstable or wobbly. I have students come in to lesson after lesson and just sit down on the throne without tightening all components, and I see them jostling around on a moving seat. Their playing suffers as a result, and in most cases they aren't even aware of it.
I don't want to go into all the different types of thrones, but I do know that most quality, heavy-duty drum thrones you'll see will have double-braced legs, a threaded height-adjustment rod, and a large mechanism that fastens and holds the rod firmly in place. It's always worked for me, and I highly recommend this type of throne base if you don't currently use it. (There are many other types on the market, and most that I've tried really don't hold up well.)
The top portion is also vitally important. There are many seats available, and the bicycle/saddle-type seat is fairly popular. Roc-N-Soc makes a popular one that I used to use, until I found it was helping to pitch my back forward in an unnatural position, throwing my balance too far forward. I replaced it with a round seat that is thickly padded and fairly firm, not soft. A too-soft seat will trick you into a false sense of comfort, and you'll sink down and squish around. I don't like to think "luxury" here, but rather stability and support.
The illustration is an example of a throne that is high in quality, yet simple. There's no back rest--I've only found them to get in the way. Also, hydraulic thrones that bounce up and down actually diminish stability, rather than enhance it. Any seat that wobbles around deliberately, much less as the result of a design flaw, prevents me from playing comfortably. It may sound a tad ridiculous, but there's a Zen nature to a strong, firm (yet comfortable) drum throne. It's extremely simple, yet perfectly effective. Adding fancy bells and whistles detracts from the quality of its function.
These are just ideas and opinions. If, for example, bicycle- or saddle-style seats work well for you, feel free to disagree. What's most important is that you have a strong foundation and good balance when you play.