OP, when you say 'G-sync', do you mean exactly G-sync and not 'G-sync compatible'? This determines whether you are locked in to Nvidia cards or not.
Microstutter, or very bad occasional frame delays seem to be as much driver related as hardware. Encountering it is a pain, and you can brute force your way past it with more/different GPU power/ram and a fast CPU/more system RAM - depending on what the root cause is. But it's often on a game by game basis. Minimum framerate, excluding these stutters, is also a determinate in how smooth a game feels and it's here that a VRR really earns its keep.
In my case I'm 'only' gaming on a 1060, but at 1440p and usually max quality settings. And on a VRR monitor it feels a lot smoother than my previous fixed RR 1080p, despite the fps being down in the high 40s/ low 50s. FPS variability is almost undetectable if I'm not looking at a counter, so if a lesser CPU results in a more variable minimum framerate then a VRR user is well shielded from it.
On CPU bottlenecks - basically the less time it takes to render a frame the higher the load on the CPU because the CPU is being asked for the render information more often in a given time period. Resolution itself doesn't have much bearing on CPU load save only that it causes a greater or lesser amount of time to render a frame. 'Bottleneck' is itself a bit of a misnomer - the process is largely sequential so CPU prepping and GPU render times are additive. We tend to use it as an indication of where you could find a bigger gain if you improved it, or to say that a particular framerate target would be possible if only the 'bottlenecking' component was improved. In reality to improve performance you need both a fast enough CPU and GPU.
And that target is precisely what the argument is above. If the OP can specify exact parameters such as game selection, quality settings, and target framerate (range) alongside already provided info such as resolution, then we can look up the charts and see what GPUs are best to pair with before (and if) there's a bottleneck to obtaining that target.
If the minimum frate rate is say the lower bounds of a g-sync window then that's something we can take into account. If the target specifies 'no microstutter' then we'd have to investigate the game in question and recommend GPUs partly based on how they and their drivers do in that particular game.