Let me try to push some thoughts into something approaching an actual answer.
Firstly - knives aren't cheap or expensive because they're inherently bad or good. It's more complicated than that.
As has been pointed out in comments, you can get a good cheap knife. You can also get a lot of abysmal cheap knives. Quite often they don't really tell you what they're made of either. Even if they do, you need to be a metallurgist to make any sense of it. One of mine says on the blade Stainless Steel X50CrMoV15. Now, this turns out to be 'pretty good' if you look up geek lists of 'what makes the best knife'. It's not 'the best' but by heck it works.
$£€ 12 from Ikea - can't complain. It keeps its edge well. I hone it when needed, once or twice a week, as I'm not an actual pro chef, just a housey cook, so I'm only making one big meal a day really. It goes through the actual sharpener maybe twice a year, maybe not even that.
Now… honing & sharpening is another thing altogether.
There are so many 'miracle' devices out there that it's almost impossible to choose.
I have never found any drag-through system that was any good for anything other than honing. My own honer is a drag-through & i've had it maybe 25 years. I'd send you straight to a shop for it… but they stopped making it years ago & I've never found anything similar. One thing you have to be reasonably sure of for a sharpener is that it's made for the type of knife you want to sharpen. As a general guide, European-style knives are set at 20° whilst Japanese-style are at 15°. Having the wrong sharpener will either blunt a Japanese blade or never even reach a Euro blade edge, so it won't ever sharpen it. In my admittedly not comprehensive search for a good drag-through, I found most were for 15° blades… but almost all my knives at the time were 20°, so it just didn't really work at all.
After 40 years of disappointment I eventually bit the bullet & bought a good electric sharpener - but at £170 that is right out of budget for this question.
BTW, you won't usually 'irreversibly damage' a knife blade by sharpening it badly, but you will make it far more of a task for either you or an expert to get it back in shape.
I really can't recommend a sharpener that isn't expensive. People will talk about using a whetstone, but if you have neither time nor patience to learn, or an abysmal lack of aptitude as I proved to myself, then you wasted your money & blunted all your knives. You can get guided blade systems, which I was once investigating - but the good ones are again out of budget.