It's occurred to me that I like games with trial-and-error gameplay. (Must be the scientist in me.)

So, what games would you suggest?

Some guidelines:
* I shouldn't be able to get through the game without making the wrong choices or having to retry sections.
* On the other hand, the game should be technically easy once the solutions are known.
* It should be reasonably obvious what to try; in other words, I should not get into a situation where it looks like I've exhausted every option and can't proceed.
* The penalty for failure should be mild, so that I can easily try again.
* There shouldn't be saveable dead ends/softlocks. In other words, I should be able to complete the game after loading a save (assuming I didn't somehow glitch the save); there should never be a situation of being able to save after the game becomes unwinnable.

So, any ideas?

All the different physics games, such as the Bridge Constructor series, When ski lifts go wrong, Poly Bridge, Crazy Machines and so on

Reading all these guidelines my recommended game for you is Ghostrunner.

I'm not sure it quite fits the bill but I had to think of Zachtronics games, specifically Infinifactory which was in my opinion the most accessible and enjoyable one.

Not sure if you've played those. All of their games (well, with some exceptions) are kinda puzzle games but depending on whom you ask they are really about engineering or visual programming - you generally have to build or design something that will do a certain job in a loop. On your way you will usually build some crap - you will feel certain that you've found a solution and then something goes wrong so you go back and iterate until it works. I'm sure that some geniuses will insist that it's not about trial and error at all but I like to think that most mortals will often resort to trial and error there. Especially when you're still figuring out the basics and wrapping your head around how all the stuff works you will surely have to experiment and fail a bit.

The cool thing is that the games are extremely forgiving. There are tons of solutions to any level, you get better ratings for building smaller stuff or using fewer components but there are no hard limits. And you can always just stop the machine and make adjustments without facing any penalty.

So I *think* these games should meet the criteria you described.

The other games I'm talking about are Space Chem, Shenzhen I/O and Opus Magnum, btw.. They all share the same overall concept but offer very different rules and tools. As I said, though, personally I've felt that Infinifactory is the most accessible and enjoyable one. Shenzhen I/O was by far the most complicated one to me but perhaps also the most satisfying (and you MUST read the manual to get anywhere). Space Chem was good in its day but I feel that it's quite similar to and was oveshadowed by Opus Magnum. Not sure if any other Zachtronic games fall into the same pattern as these four.

Edit: Oh yeah, TIS-100 also has that same pattern but I haven't played this one yet. It may be even more complicated and dry than Shenzhen.

The classic Incredible machine https://www.gog.com/game/the_incredible_machine_mega_pack

Another sierra classic, Gobliiins https://www.gog.com/game/gobliiins_pack .Though that one may have a few non-obvious solutions.

Zack & Wiki: Quest for Barbaros' Treasure would be another example of the complete the puzzle area type game play (more childish in plot) and is available for Wii or the Wii U. Enjoyable puzzles for as long as i played it.

Some adventure/quest style games might meet your needs. Many of the Wadget eye games are fairly logical in nature. I remember enjoying Techno Babylon for the most part.

I was going to say that, in fact I agree with everything in this post 100%, with the exception that I haven't played Shenzhen I/O.

Lemmings.

Kerbal Space Program*

(In sandbox mode with unlimited resources.)

Let's see here, there's several games in a class like this, "Fall/Fail Forward", where you aren't punished for failure in the typical manner. Like how if you're KO'd in Super Mario RPG, you don't lose any experience progress.

Ikaruga?

The Incredible Machine

World of Goo

Reventure
Reventure is essentially a puzzle game where you have to find 100 ways to end a run, ranging from falling in a pit to rescuing the princess from a dragon in the depths of a dungeon (and some humerus bits). In the end, you basically retry this over and over till you found all ways to end a run.

Return of the Obra Dinn
In the Return of the Obra Dinn (a game of fantastic quality) you have to investigate the identities and cause of death of about 60 people. Presumably you can get everything right without ever guessing, but in practice I did do a bit of trial and error. Identities get "locked in" whenever you got 3 right, so if you think you have 2 you are pretty certain about, you can do some trial-and-error to get a 3rd in.

Gorogoa
Gorogoa is a puzzle game where you have 4 frames that you have to try to alter till two or more of them interact in a scene to progress the game. Again, the game mechanic is absolutely stunning and unique, much like Obra Dinn and I would very much recommend this and the latter to anyone, just based on the quality and uniqueness of these games.

That game does look rather interesting.

(Unfortunately, it does suffer from the fact that the music in the trailer is of the sort that gives me headaches.)

Tower of the Sorceror fails most of your guidelines, but I think it is a good trial & error game.

It is focused on judging how to expend nonrenewable resources to proceed forward - but the various obstacles take differing amounts of each currency. Determining how to spend and replenish your stockpile is key, and learning the layout of each level is important. Memorizing multiple levels is key, since you not only have to think about the current level's cost, but also what is required for future levels.

Tower of the Sorceror

Well, if it helps, non of the puzzles involve sounds if I remember correctly, so you could just turn it off.