How about this, ran across it a few minutes ago so started a post with it in r/buildapcsales
https://www.reddit.com/r/buildapcsales/comments/186kl8l/cpuintel_core_i512600kf_core_i5_12th_gen_alder/
Your present MB may already have the needed Bios for that, double check on the Gigabyte website
Scanoe
https://www.reddit.com/r/buildapcsales/comments/18693hd/prebuilt_msi_codex_r_gaming_desktop_intel/
How about something like this. On Amazon the 13400f is $200, the 4060 8GB is $300, that is a decently priced Prebuilt.
Your 12100f & 6600 Complement each other, upgrading one of them will just cause the other to be a Bottleneck. I'd save the money for a complete overhaul.
A 13400, 13500 would allow you to keep your MB & Ram, that 12600k would work on your MB as well, you just wouldn't be able to OC that K. The 13600k might be a bit much for your B660 due to Heat Issues.
pc-builds.com lists that 12600k as a Bottleneck for a 4070 at 1080p, I'm not sure If I believe that or not, I'm guessing that pair would be fine for Gaming, possibly not professional type work.
Comparing a 4070 to that 4060Ti, you'll more than likely kick yourself after buying that 4060Ti, the 4070 is a good bit better, albeit more expensive as well.
A 13400 or 13500 would be a large upgrade to that i3 of yours, and you could stay with your present Motherboard and Ram, you would more than likely need to Flash to a newer Bios though.
What Video Card do you have though?
If your CPU isn't the Bottleneck upgrading the Cpu wont help much.
I see your point, I really don't like leaving my old pc parts laying around collecting dust either, what I do is take my previous pc parts, put it together as Budget Builds then dump them off to Family and Friends whom do not know how to build pc's, works like a charm :P Seriously, I do usually give it to them for Free though.
To better answer your question:
Your i5-3470 is a 10+ year old platform using only DDR "3" Ram, that platform is getting too old to bother with.
I looked into Bottleneck, that 660 Ti is already to weak for that 3470, So....
A couple comments I've seen in this Thread could help you to not have to throw it all way.