You don't really need a CPU cooler as ryzen processors come with fairly decent ones - only reason to get an aftermarket one is if you're overclocking or want something quieter. Also you have a GTX 970 already right? The RX 580 performs very similarly so you'd be better off just keeping your current card and upgrading to something else down the line.
Don't think that case will fit a DVD drive by the looks of it either - Need one with an expansion slot or could just get an external USB DVD drive if you're not using regularly
Reusing the GTX 970 is an option, it works well for the needs we have right out.
The case says it supports a 5.25in ODD bay and you can see it in the close up pictures.