I'd look at a B550 board in the 125-150 range...you'll get a solid VRM setup capable of handling any Ryzen 5000 chips without issue. Look at the hardwareunboxed channel on youtube as they've tested a lot of AMD boards over the last couple of years so you'll know what to avoid.
As far as manually overclocking the 5600x there's really no need as AMD has invested heavily in optimizing performance out of the box. To get max performance simply buy a really good CPU cooler, enable PBO (technically overclocking), and let the chip do it's thing...essentially all you have to do is manage heat and the CPU will manage voltage and clock speed for you.
Pairing the 5600x with fast 3600 or faster memory with tight timings like cas14 will really let the CPU run at its best and it will push the 3070 as high as it can go.