Most people either use google as their search engine, or one of the "privacy friendly ones" (ddg, qwant, brave, startpage, ...), or use self hosted or publicly available metasearch engines, like searxng, or whoogle, etc.
This websites lists out websites which have their own indexes, and which depend on big providers.
Why YSK?
It is good for your privacy to not use a big provider like google, which now prefers to serve you ai generated ssummaries, which are based on a few giant websites, and this is not good for a open web.
I am also a person who almost always uses "(insert query) reddit" to get better results, because I mostly do not want SEO spam, and reddit results used to be human generated content. Now even that is hit and miss. Also, reddit made a deal with google, so for newer results from reddit, you can only get them from google.
Then we have the "privacy friendly ones" which most of the time are wrappers for other bigger indexes, for example ddg famously uses bing, brave "suppliments" (read this suppliments as almost always) it's results from google, startpage is basically a google frontend, etc. Brave, qwant, and few others also claim to have their own indexes, but they are small and not rich as google and bing. Also, wwhen you think about it - what is their business model - how do they get money for the search apis - most either serve ads or have some form of tracking. Also, bing has "kinda" closed it's search api (not really clear about this), so many of these privacy friendly options will have to either switch to google, or only serve using their indexes.
Meta-search engines kinda seem like better options, as you can run searxng on your own machine, or use the public ones, but it still has problems. You are still bringing the big providers traffic, which makes their advertisement clients happier and prefer them over smaller search engines. If you use a public instance, then it is good for your privacy, but the public instance would now generate a lot traffic, and often get banned or rate limited, and hence you can not rely on them. If you use your personal instances (I did this for a long time), you will still be tracked as your IP is still visible. You avoid their annoying ui and popups but still are tracked.
So what should you use?
You can only decide this. I would prefer something which has a reasonable business model - if they do advertisement, that should ideally be non tracking. Ideally their client and server code should be foss (so you can verify their claims), or have paid plans or apis if you do not want ads.
For example, Kagi has only paid plans, but I do not prefer or use them, because they are expensive (5 dollars for 300 searches per month or something similar. I am from one of third world countries, and 5 dollars is a lot. plus 300 searches seem less to me) but that is subjective, and your privacy has a price, so this is not neccessarily a objectively bad thing. But their code is closed source, and they do not completely use their own indexes.
I have also used Mullvad's Leta search engine for about a month, and they are now effectively frontends for brave search or google (you can choose). Their business plan initially was that Leta was only available to their VPN clients, and VPN subscription would supplement the search cost. Now they have it available for free, so I do not really understand their business plan (maybe the number of clients they have is large enough, and number of leta users is small, that they can afford to run leta for loss, and maybe as possible advertisement for mullvad. Mullvad to me is a good privacy centric company. I am not their client, but they seem to be trust worthy. You can try them, but you would still support some big provider.
You can also try the independent search providers listed in the article. They are often small, serve bad (subjectively speaking; your taste regarding search engines is also heavily tuned to google like results because of years of exposure to it) results, but using them also supports open web (you would often find that these smaller providers do not have good indexes for big websites, and sometimes it is intentional, sometimes it is a byproduct of them being careful, or the websites banning/rate limiting then).
I have now started trying stract, and will try others too. You should also consider trying some independent search engines.
In my personal case - I have a offline setup where I have large sections of wikipedia and a few other websites (like programning language docs, or my favorite manga wiki, will be adding much of stack overflow soon) available offline, and I use my custon launcher to search through them (faster then searching them online). I bookmark a lot of sites (~ 2000) and do this to stop searching the same stuff over and over again. This has reduced at least 30-40% of all my searches. But I still need a search engine for anything I do not have currently, or stuff I do not/ can not get. I am trying stract, because it is open source, they seen to have some fine plans for business in future (non tracking, current search term related ads or subscription service ; currenlty they are running on previous funding from nlnet); search results are acceptable (not good, but servicable); and finally - it is written in RUST (I an a rust fan). I am not affiliated with the project, but just spreading a good word because I just found them, and could not find much online.
PS: I am not used to writing much, and not a good typist. Please forgive the brevity. Feel free to correct me, both on spellings and content