The handplane is what I'd use.
If you have a perfectly flat bench to plane on or check with, then its a much simpler process even for a newcomer, as the bench tells you where the high spots are.
You can even burnish the high points, or a step further use some crayon or graphite.
You must have a good lamp, I like a long reach angle poise for the job, if you don't plan on spending as long as you want safely messing about and taking thin shavings.
The black/dark crayon comes off with two rubs or supposedly WD40 if you had something other than a wooden top.
The crayon/graphite will teach truly how heavy a cut one can make with a light setting on the plane.
A good project and serious skill builder is making a pair of parallel straight edges, no shorter than the longest thing you wish to plane.
You can get twice the tolerance of your bench with the two surfaces,
and that's well beyond what you can see, as any gap will be doubled.
I use a few blocks for shimming the middle of this thin bench top until its good.
The parallel beams can be checked for straight by flipping one around to ensure any possible spoon factor happening..two crooks in the timber matching, should I say.
Just watch David Charlesworth's videos for planing methodology, simply no one better at instruction on precision planing, hands down.
He will make you a pro in about half an hours watching,
you will be fimiliar with "stopped shavings" and through shavings, watch everything you can find if you want the best.
just don't follow anyone else as most of the guru teachers are dishonest, plenty of those guys.
Cosman is also skilled and honest , (strictly regarding the work), but he would have you convinced you need to buy half of Canada.
And then take David Weaver's advice regarding setting a plane, and you won't have any tearout and an unbeatable sheen with the use of the close set cap iron.
There really is a difference using the close set cap iron if you want chatoyance, but you must follow the rules of setting up.
Take anyone elses word other than David W 's (youtube username) with a pinch of salt bar a few, which I can name for you.
You can see what's called the "influence of the cap iron" in these folks videos, which is * unbroken shavings coming up and out of the plane *
and not curling around.
David made a good document called "Setting the cap iron" on a woodcentral webpage for a quick summary.
TheEnglishWoodworker (just don't look at that misleading thumbnail)
Brian Holcombe, knows a good thing when he sees it.
Mr Chickadee, has touched on the subject, a man of few words.
Franks workbench, seems to have the hang of it.
Hernan Costa, Spanish guy I think, obviously knowledgeable about the cap iron, or whatever it's called in Spain.
Seekelot, a man who has done some testing before, one of the odd ones that doesn't prefer 50 plus degrees cap iron angle, not sure if he works exotics which would explain things.
I think I recall Matt Kenny making some influenced shavings in some video before.
And an even newer youtuber to me, but has been around a long while is Dusty splinters, he has quite a lot to say about the cap iron.
I haven't seen anyone else who actually uses the cap iron to its full potential, but seen plenty of folks saying they do, when infact they are only giving bad information, like suggesting having a fine mouth, which just won't work and has likely put many off.
So be warned about taking advice from anyone other, it should be plain to see from what I've mentioned.
If you see anyone using a scraper for anything but refinishing or veneering, or anyone dodging a knot on anything but the heaviest jack/scrub planing for flat work, then they are missing out and should see what all the fuss is about.
All the best
Tom
