All of these are products I've used extensively for many years. They are all good in their given range of use and desired results.
M81 has absolutely no "cut" beyond the pressure you put on the applicator. It's purely a beauty product.
The 3M Foam Polishing Pad Glaze will have a small amount of abrasive or cut. It does tend to hide minor marks with a machine, but I never liked its results by hand. It worked so much better with a rotary than by hand.
Meguiar's M82 is a mild cleaner similar in cut and result to the 3M FPPG. It does work well enough by hand that I would recommend it in this case. It won't remove much, even with a rotary machine, so expect minimal swirl removal when worked by hand. If you just have some light spiderwebbing to remove and fill before waxing, this is the one.
M80 is the next step up in cut. It's a very good product to use by hand. It has a lot of oils so it keeps the surface lubricated while you work it. If you have some defects to work out by hand, it's more likely that you'll get it done with this product rather than M82.
M83 isn't one I would recommend using by hand. I think Meguiar's says you can, but I wouldn't advise it unless you:
1. Have serious marks you want to really work out by hand
2. Plan to follow with M80 or M82 to help clean up what M83 left.
*BY HAND*, you'll have to work all of these choices (except M81) until it breaks down. It's not going to be wipe on and off like M81. M80 is the most forgiving if you don't get it worked down completely.
If I had to choose one of the products you mentioned, I'd say M80 due to versatility and ease of use. Follow it with any of the three LSP's you mentioned and you'll be satisfied.
On the LSP choices, M21 is more expensive than the other two, but gives a good look and is durable. M26 gives a warmth and depth, especially on dark colors. It's not quite as durable since it's basically a wax and not a full synthetic like M21.
M20 has some very mild cleaners along with the sealant it puts down. While it's not a true cleaner wax, it's almost one, so I'd not recommend it according to what you said.