Ok, it seems there's one thing I hadn't noticed before:
Under 25", G-Sync doesn't seem to be available with VA or IPS. Only TN. And I have no idea why. Problem is, I would definitely recommend IPS or VA. Then again, for gaming I would definitely recommend FreeSync or G-Sync, as well. And with your budget, you could even afford nVidia and its G-Sync premiums.
So (if going with nVidia), I think you'll now have to decide whether you'll compromise on TN, or forego G-Sync. There are two 24" 165Hz 2560x1440 G-Sync models, both TN:
Dell S2417DG
AOC Agon AG241QG
I don't recommend either one, just telling they're the options. There's also the FreeSync version of the AOC called AG241QX, but that's also still TN. And these three are apparently the only <25" models with 1440p and FreeSync/G-Sync (at least for the time being). If you forego the 1440p resolution, then at least the FreeSync side options open up.
Among those, the Samsung C24FG70FQU stands out as the only 144Hz non-TN, being curved VA. But it also has quite a lackluster FreeSync range (70-144Hz). Then there are for example the 60Hz 4k FreeSync options of
LG Electronics 24UD58-B (2016 IPS)
ASUS MG24UQ (2016 IPS)
Samsung U24E590D (2015 PLS/IPS)
Samsung U24E850R (2015 PLS/IPS)
Then there are few 75Hz FreeSync options, all IPS:
LG Electronics 24MP68VQ-P
LG Electronics 23MP68VQ-P
LG Electronics 22MP68VQ-P
Acer BE240Y
But that's about it.
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... As such, I didn't realize how limited the 24" range is. I've usually only dealt with 27", and the options there are quite numerous.
Personally, I would go with the FreeSync compatible Samsung C24FG70FQU and get an AMD GPU. For those who want G-Sync and can compromise for TN, the Dell S2417DG seems like a viable option.
Ps. Now, there is currently a standard war between the FreeSync and G-Sync. But with the current pricing differences, FreeSync has begun to rise as the winner. And this is just an opinion, but nVidia will eventually have to start supporting the FreeSync (or the Adaptive-Sync it's based on) with its GPUs. Problem is, that might not happen anytime soon, so you might have to wait a while.