I presume that you are looking for better gaming performance.
What is the make/model of all of your other current parts?
What is your budget for this upgrade?
Games are limited usually by the cpu or the graphics card.
For graphics, a 3060ti would be a nice and appropriate boost over a rx580. If you can find one at anywhere MSRP.
All of the 3000 series cards are being scalped and hard to find.
Modern graphics cards need only a pcie x16 slot to install.
The very high powered ones may need added psu power, but your 580 is a power hungry card so whatever psu you now have should be sufficient.
On the cpu side, much depends on the types of games that you play.
You now have a very good processor with 8 threads and a single thread passmark rating of 2533.
Few games can make effective use of more than 6 threads. They are mostly multiplayer with many participants.
Here is a link to your cpu upgrade options for your motherboard:
https://www.gigabyte.com/us/Motherboard/GA-A320M-S2H-rev-1x/support#support-cpu
About the strongest reasonable upgrade might be a r7-3700X.
You will get 16 threads and a single thread passmark rating of 2690.
That does not seem like much worth it to me.
Anything stronger will require a motherboard change.
A r5 5600x would give you 16 threads and a single core rating of 3382.
A very good boost, about the best you can do today.
Unfortunately, again, the scalpers have made the 5000 series chips hard to find, particularly at anywhere near to msrp.
On the intel side, a 9700K would need a Z490 based motherboard.
9700K has 8 threads and a single thread rating of 2912.
I would not go that route.
Better to look at 10th gen i7-10700K 16 threads and single core rating of 3087.
If budget is an issue, look at the i5-10600K with 12 threads and a single thread rating of 2941.
It is a good budget gamer, here is a review:
https://www.tomshardware.com/reviews/intel-core-i5-10600k-cpu-review/5
You would want a Z490 motherboard with either one.
Unless your cpu upgrade is urgent, I would wait a month or two for intel rocket lake to be launched.
Leaked benchmarks show rocket lake new architecture to be faster than even the r9-5950x:
https://www.techpowerup.com/276459/...rforms-amd-ryzen-9-5950x-in-single-core-tests
Interesting times.
Patience will be rewarded.