Intel or AMD for a CPU is a little from column A and a little column B. On the top end, AMD releae a new chip and tale the lead, then Intel release a new chip and take the lead then rinse and repeat. More mid-range it gets a bit murkier as I’m not sure on the price to performance.
I’m also not certain of prices in USD but for a similar budget here you could get something like a Ryzen 5600x or Intel 12400 with appropriate motherboard. I’d recommend 16Gb RAM with as fast as you can get, probably 3200MHz at minimum. I’d also recommend getting an M2 SSD as they’re super fast and you could re-use your existing drives as additional storage.
PSU it depends what you end up speccing and future proofing you want to do. Once you have a rough idea of spec there’s plenty of PSU calculators online. I’d guess you’ll only probably need 500-600W at most. Though depending on how long you expect the PC to go for and if it will see futude GPU upgrades, it’s cheaper to spec higher watt one now than have to change in the future. Corsair, Seasonic and SuperFlower are generally the top brands but it does depend on specific models.
Case, I’m sure you could re-use the existing one as not much really changes in cases design except for the addition of tempered glass and generally a reduction in hdd bays. So up to you on if you want to switch cases.
GPU, I’d imagine you could get a RTX3060. Dependong on USD pricing and if you don’t want a case, you might be able to go for a 3070. Though even a 3060 is 4x or 5x faster than a 480 so would be a massive improvement.
If you go on PC part picker you can spec a PC and share a link for us to look at. For some reason, on my phone, it defaults to UK so can’t put a US build together.