Is a RTX 2070 Super good with the Ryzen 5 3600x with a $500 budget for a GPU?

The whole thing about the CPU in a gaming rig is sometimes overblown because you don't need a great CPU to attain 60fps. Even a Ryzen 5 2600 would do the trick for 60fps. The only time you would need to worry about the CPU is when you're trying to drive your framerates up to feed a 144hz monitor The Ryzen 5 3600x is slightly behind a Core i7-8700k in gaming, but only when the 8700k is at it's stock speed which is 4.3ghz on all cores. The Ryzen 5 3600x does a fine enough job if you're going to play games on a high refresh rate monitor. 

The new Ryzen 3000 processors do run a little bit hot so you might end up looking for an aftermarket cooler. 

I've had a few systems with AMD processors such as the Phenom II and Ryzens and I've never had any trouble with those. 

They might work together okay with the correct motherboard and power supply.  But "good" might depend on what you will do with that equipment.  Games, editing, music, YouTube, office, Internet, utilities, other?  And what you might connect to the video port and what you want to see at some screen or screens, resolution, refresh rate, audio sent along too.