Best CPU upgrade for ASUSTek PRIME H310M-K R2.0 motherboard?

@emz_20_02  Your motherboard could support up to a 9900K.  An 8600K/9600K or above would be effectively equal in terms of performance.  Processors tend to fail right away or not at all, at least not during and past their useful lifespan, so getting a used one that works immediately is only a very small risk.

However, far more important is the graphics card, which in your case is the limiting factor by a wide margin.  A used GPU along the lines of a GTX 1050 ti or 1650 could be under $100 AUD (I don't know what the market is like there, but have a look at Ebay and Craigslist) and would make a much bigger difference.  In fact, without upgrading the GPU, most of the improvements from a faster CPU would be wasted or hidden behind more obvious graphics-based performance issues.

I wonder if the inability to get to 144 Hz is related to the GPU as well.  I'm not sure, but I wouldn't be surprised if the GT 710 simply couldn't handle it.

If you do want to upgrade the graphics card, one important detail is the computer's power supply.  Its wattage will determine how powerful a GPU it can support.  Most mid-tier GPUs require a supplemental power connector, but the 1050 ti and some models of 1650 do not; plus the actual power delivery matters here.  So please let me know the specs of the PSU.

One other upgrade that would make a big difference is swapping out the HDD that you probably have for a solid state drive.  This would improve load times and general use, although Sims 4 would run pretty much the same once loaded.

As for whether it's better to upgrade this system or get a new one, that depends on how long you want to keep this and how much of an improvement you'd like.  You could certainly upgrade the GPU and call it a day, then consider a new system in two years.  If you're swapping out the CPU and adding an SSD as well, that becomes the point where it's probably worth getting an entirely new computer.  Not that they'd be the same price-wise, but the investment into this system would be more than it's worth in the long run.  On the other hand, if prices for used components are actually good where you are, you might be able to cobble together a significant upgrade for a low-enough price that you're satisfied.

Thank you puzzleaddict, I really appreciate the thorough response. 

The PSU is an Axceltek AP500 500W.

So, would it be worthwhile to upgrade both GPU and CPU? Or mainly just GPU? Together, I'd be willing to spend about $500-600AUD at this stage. My partner would be taking on the computer after me so it wouldn't go to waste. From my brief googling, it doesn't look overly difficult to install either of these.

The 1650 is around $140-$175AUD which is perfectly reasonable. I'd be happy to spend a bit more if it will provide better quality and less lag. 

SSD might need to wait for the upgraded version as I don't really have the experience or the capacity to make too many changes to this one, particularly if I need to troubleshoot.

Thank you again for your help.

@emz_20_02  If you want the best performance this system can reasonably offer, then yes, I'd upgrade the CPU to at least an 8600K, that is if it's reasonably cheap.  (An 8400 or 9400 would be a smaller improvement and possibly not worth the price.)  If it's currently more money than you'd want to spend, you could hold off for a bit and keep an eye on prices.  The faster GPU will have a bigger impact anyway, and you might decide the game runs well enough for you without the CPU upgrade.

What a faster processor does is clear the usual game engine backlog more efficiently.  It's not always easy to see when this is happening, but it most often appears when a lot of calculating needs to happen at once.  For example, if you own Eco Lifestyle and don't turn off NPC voting, the game will slow down as the votes are tallied and the relevant Neighborhood Action Plans are applied.  And then it will (should) go back to running as normal, at least until the next issue.

The other question is whether your power supply has a supplemental PCIe connector.  As I mentioned, the 1050 ti and some 1650s don't need one; you'd have to check the specs of the exact model you're buying.  (Let me know if you need help with this.)  If the PSU does have such a connector, and a 500W unit probably does, then you wouldn't need to worry about this detail, and you could also consider getting a GTX 1060 or 1660 (any flavor) or 2060 if the price is right.  Neither is necessary for ultra settings, but you might enjoy the benefits of higher framerates on your 144 Hz monitor.

To be clear, there are two types of "lag" here: delays in rendering and delays in processing.  The first is mostly GPU-dependent, and the second is entirely CPU-dependent.  Your current CPU is decent enough that I wouldn't expect any major issues with it, not like the GPU where there's a world of difference between the GT 710 and the cards we're discussing here.  So you could reasonably skip this upgrade, especially if you're happy with performance once you get the new GPU installed.

I do want to say that a new SSD wouldn't be as much trouble as you might imagine.  It would need to be a SATA SSD, which means connecting to the motherboard and the power supply (the latter could probably use the same cable as the HDD does now).  Beyond that, reinstalling Windows sounds intimidating but can be done quickly and easily; you only need a USB 3.0 stick you don't mind erasing.  Then you either download the chipset drivers from the motherboard's support page, or better yet, you download them beforehand and store them on a different USB for offline installation.

If you're not ready to do that now, keep it in mind as a possible future project.  It's the kind of thing you can get right the first time with nothing more than a YouTube guide and some focus.