I don't know what "cheap" means for you, but if you'd like to put a 5K
retina monitor with that 2023 Mac Mini, the
Samsung one is on sale for what I consider "cheap" and it would give you a much bigger 27" monitor instead of the 21.5" one you were seeking with that iMac.
And unlike that iMac screen, when that Mac Mini ages out and you have to replace it, you
WILL be able to attach the replacement to the Samsung... even if you went PC. Bonus: if you happen to need Windows too and ARM Windows is not enough, that monitor has TWO inputs so you could connect 2 computers to it... or the Mini and an AppleTV or game console, etc. Bonus #2: it also has some TV apps and a remote so you can use it like a 27" television too.
However, you can budget less than half of that price for a 4K monitor if "retina" isn't important to you. I've helped people go both ways and 4K can look quite good even if not retina. Find an ideal one by doing searches for "best 4K monitors 2024" and similar and then reading reviews for any of interest. Note that best is not necessarily defined in full by "cheapest", so you are advised to dig in and get a sense of a mix of features & benefits rather than just jumping on one with a cheap price. For example, do you want a:
- built-in webcam or perhaps add that as an accessory later if desired?
- great speakers built in or perhaps add good ones as accessories?
- a good hub built in?
- faster than minimal refresh rate?
- Etc.
Since this purchase might be the monitor you keep using with your NEXT computer too (just like you were wanting to do with that iMac screen), you might want to go for a great one vs. a cheap one that you may then feel compelled to replace on down the road.