Opinions on 3rd and 4th gen Intel
I gamed on an i7 3770k until middle of last year; And as an accomplished PC builder, I watched the market for all 8 years and never felt the need for an upgrade; And followed all the new processors in that entire timespan, I feel like I am more qualified to chime in here than almost anyone else. As someone who lived with, and gamed with the i7 3770k almost daily for 8 years, I can tell you first hand exactly what to expect from these generation of parts. Even in the past half year after upgrading to an 11th gen i5, I have not felt much of an increased performance from my CPU.
If you're planning to allocate any amount of budget in upgrading the planned rigs, you're best off following the number 1 rule of building a gaming rig; Allocate the biggest budget to your graphics card. I would say that holds more true in your case than anything else combined.
In my 8 years experience of running the i7 3770k fropm 2013 until 2021, majority of that time of which it was paired with a GTX680 : I can tell you the 3rd gen processor felt plenty powerful, and I played minecraft extensively throughout several of those years so I can speak first hand for that title. It was the GTX680 that was screaming and dying in newer games; as soon as I upgraded to my GTX1080, the old i7 3770k kept trucking along just fine, and honestly still would to this day if I didn't upgrade still. I did not feel like any game would have benefitted all that greatly from the added CPU processing power. Hyperthreading is nice, but honestly it tends to be only a fairly minor upgrade in performance, even in games like minecraft. Minecraft is considered quite CPU dependant and benefits from more cores/hyperthreading, but even then you're not going to see double the framerate from having an i7 over an i5. Maybe in the moderate 10% fps increase. Plus I'm assuming you're not going to be giving her any crazy high refresh rate monitor anyway, so she'll be running between 30~60 fps which is extremely easy for even this generation of processors to push, and assuming you'll be giving her a cheapish 60htz display anyway, there's no reason to aim for higher unles she's got aspirations to be a competitive FPS player or something where input lag matters to her (which is the main benefit of a higher fps above the display's refresh rate)
For this generation of CPU's especially, it's well documented by now that the RAM, and Motherboard have minimal effect on gaming FPS, only on overclocking performance. And even though these chips do overclock well, it's actually not necessary to flog these older chips unless you're an enthusiast and enjoy overclocking; It's too much hassle, and risk of instability in a family member's rig just causes more headaches incase of bluescreens and crashes in the longrun. I would not bother doing anything but the mildest overclocks on these chips, and mild overclocks give almost negligible FPS improvements, especially again, as your main bottleneck is going to the GPU based, not CPU based. And even if you did overclock, the extra money spent on K-series CPU, beefy cooloers and fans, better PSU's and better motherboard chipsets; At the end of the day the parts needed to overclock reliably honestly detracted from any cost-efficiency claims that overclocking could have held. Again, not worth the effort of overclocking, especially on a rig where if something goes wrong your daughter has to come whining to you.
That 660ti is the ONLY part you should be considering replacing. Until you replace that gpu, don't even think about spending even a dime on anything else.
So unless your daughter is a snob who requires 200+ FPS to play and have fun, she'll be fine running vanilla or light minecraft modpacks with the current processors you described. From memory, my i7 3770k and GTX1080 combo was pulling around 90~100 FPS with moderate settings in vanilla minecraft, in closed spaces, with rare dips to 30 fps during explosions. Your daughter's currrent rig should be within ~20% of my old rig. The GTX660ti is by far the weakest link here, and evidence of this will stick out like a sore thumb once she pushes this kind of rig with even a moderately graphic-intense game. In fact, I would wager even the newest Sims games will display some signs of this.
I would say use whatever board and cpu you currently own, and let your daughter grow into some more graphically intense games, and when she does, keep that fund ready for a GPU upgrade.
So even though this is a gross oversimplification; I would say the 3rd gen i5 is fine to handle anything up to a GTX 970, or GTX 1060. Only once you find yourself with a GPU of that spec or better, should you look into a CPU upgrade. If my 3770k felt like a good compliment to, or at least, only a smallish bottleneck to a GTX 1080, the i5 could probably pull adequate gaming FPS with at least a GPU of this spec range. Obviously it'll depend on alot of other factors and the exact title, but this should be your rough average with any new title your daughter may play.
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