This part can be quite challenging with so many possibilities, working and non working versions of the same card. And success (including partial and during earlier development) posts scattered all over.
Some risk to buy pre-flashed cards. Read link
Best choice is M4000 ( link ) M5100 more rare and more costly
Best choice is WX4130 ( link ) But already pricier and more rare.
M4000 / M5100 can be used on 12,x but must turn sleep off to avoid the sleep/wake problems.
nVidia cards (eg K1100M) are fairly abundant and enable running OCLP Big Sur well. Sounds like more problems beyond Big Sur (I have not tried)
The stock iMac with original GPU can run OCLP Big Sur pretty well with a couple of graphics setting tweaks ( link )
This table is work in progress. I've done M5100 in 11,1 M4000 in 11,1 and 11,3 and WX4130 in 12,2
Its pretty clear AMD is generally the best choice if wanting latest macOS. nVidia have always charged more for their GPUs thus Apple naturally worked with AMD more. This means much less native macOS nVidia drivers exist. OCLP and Metal GPU vBIOS efforts are not driver development efforts. They depend on Apple having produced drivers for the GPU for some older version of macOS.
For those willing to accept <= macOS Big Sur, cheaper nVidia Kepler generation cards become possible.
Besides "google" Here are a couple of useful tips
Here is how to decide Post #1's GPU choice selection info
Note you can avoid most of this choice complexity if just choose the simple low cost easy to install cards I've outlined above
Searching the macrumor thread with a particular GPU to find the history of posts. Here is one for AMD M5100 and nVidia K1100M (Kepler) These will provide a time sequenced posts on these cards. Earlier ones are often during vBIOS development phase, later ones more likely to match your experience. Here is how to search this thread only
Youtube has some guides that are quite good. But be cautious as posting date likely will show older processes and tool user interfaces. Some might be very close and exact to the latest experience while others may contain out of date or incomplete info. But nevertheless, these are valuable.
Might come across come one installing your card of interest in the thread. Click on their name, find all their posts... read what happened. Unfortunately sometime people don't follow up with results :(
Try to find guides (posts or videos) for the interested GPU card. Just note the potential of some out of date info and incompleteness.
In general, newer posts are likely to reflect closer to your experience as tools and processes improve. For guides, typically later posts/videos are closer to your likely experience.
All these GPUs requires flashing its vBIOS to work well with Macs. This work is done by some really capable devs but at some point, they are done. All the progress during dev and users posting success after completion are on the web. So posting dates matter. Its useful to make a little note file with links and dates to organize as the # of webbrowser tabs will get crazy high and easy to get confused and lost.
Here is one I made for M5100
main link https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/
M5100 search https://forums.macrumors.com/search/4463060/?q=M5100&t=post&c[thread]=1596614&o=relevance
3/26/21 GRML USB boot stick firmware flash https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/page-545?post=29723850#post-29723850
10/21/21 firmware post https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/page-662?post=30485318#post-30485318 Firmware location link on bottom : NEED to click IMAC-EFI-BOOT-SCREEN on top (left of "public") to reveal the files for some reason.
12/3/22 guide #1 https://www.youtube.com/watch?v=n9koG8p9Ch0
Of course this list looks quite nice after success and may look messier from the start. Just noting using this useful method.
Finally if you did now for M5100, will find my post :)
1/24/24 https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/post-32882827
This is pure speculation on my part with knowledge in semiconductors manufacturing processes.
These low cards are made later than original iMac by 2-5 years. Chip process advanced and runs cooler IF you avoid big powerful chips (low budget naturally avoid these haha) The M5100 is considerably smaller looking chip than original in my iMac and is a later more thermally efficient chip process.
So I wouldl guess thermal issue might be mostly resolved even if using used low end metal cards. For big powerful metal cards, its probably a different story. GPU makers struggle with BGA chip soldering issue even today with biggest hottest chips. TV chips (with GPU inside) struggled with this > 2015 as TV makers use older less thermally efficient chip processes.
Buying pre flashed GPU cards an eliminate one complex step so definitely useful for the more novice. Do read further on vendor choice.
While M4000/M5100 are easy for vendor to flash. WX4130 is likely more challenging with a lower profile flash rom which typical low cost flash rom clip can not attach to. So not sure pre-flashed WX4130 are being sold.
Chinese goods and services always have multiple grades. Better grade is always more expensive of course. It is the same for pre-flashed GPU card. There are knowledgeable vendors with more reviews, sales, and experience.
As of Feb 2024, Mac-Part Store seems to be a high volume pre-flashed iMac metal GPU vendor. Subject to changing market conditions of course. Please make your own evaluation.
I bought a M5100 from a new vendor with lowest cost. They flashed the wrong vBIOS AND pressed the smaller bolt inserts in the 4 corners of the X bracket. Card has random hangs after I flashed the correct BIOS. I'm guessing the pressing effort could have damaged the board if inexperienced.
So buying one from vendor with good reviews for iMac.
Regarding claiming tested... I think its doubtful. Unless someone mades a test jig without pulling the screen everytime (seems unlikely for a $30 used product) I doubt they tested on an iMac. But again, no choice. Better vendors at least won't sell you from a pile of known failed cards.
All Metal GPUs will be 2 or more years newer than original iMac's GPU. Newer GPU will use newer semiconductor technology able to run more computations for smaller area and less heat.
Even the smallest and cheapest metal GPU replacement is likely to be >= iMac's original GPU with lower heat output.
Especially with focus toward smaller cheaper metal GPUs in this site. No need to have thermal concerns.