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My take on scratches, scuffs and general signs of wear and tear is the it shows you use the damned thing (whatever it is) so there's no need to worry about it too much, but of course some damage is really unsightly and begs attention.
Lots of abrasives are available to do the polishing that you want to do, but do be aware that they work by removing metal from the surface that's being polished. You'll see a black material on the polishing cloth or whatever and that's because metal powders are generally black.
Because metal polish removes metal (that's why you can sharpen an edge with it too) it stands to reason that if you have deep scratches you'll have to remove a lot of metal to make them disappear.
That's another reason I don't particularly care to polish things like hand tools, I like them to have left on them as much as possible of the metal that they were made with. But as I might use a knife for food prep I do like knives to be clean, and it is easy to clean a polished blade.
You haven't mentioned the material of your blade, but some metal polishing materials are especially designed for particular types of metal. Some are also sold in several grades to speed up the polishing process, so if you have a lot of deep scratches you might want to start off with a coarse grade abrasive, which cuts faster but produces a rougher finish, and work through medium to fine to gradually recover a mirror finish. Generally though you'd have to be in dire straits to need much more than Autosol for a knife blade.
It does seem like you're looking for a mirror finish, but it might be worth considering alternative finishes, such as satin, blasted, pickled or a patina. They will mostly be more forgiving or (ab)use than a mirror polish, so you can cut down on the amount of work you're making for yourself by choosing a diferent finish, yet still have a reaonably good-looking bit of kit. A lot of people like a patina on a steel like O1. I don't personally, but most of my knife blades are some kind of stainless.
If you do set to with polishing abrasives such as Autosol, give some thought to using power tools to speed the process. By hand processes alone, trying to take a large amount of metal even from just a few square inches of steel can be pretty tiring. Just a buffing wheel in a low-speed electric drill can make a world of difference.
Of course always take great care when polishing a sharp blade. It's all too easy to take off a slice of your anatomy.
Finally take care of the blade when it's not in use. Even stainless blades can develop unsightly and potentially damaging corrosion if they're badly neglected.
