If I were to get this under $1000 as a hard maximum, this is what I would do.

PCPartPicker part list / Price breakdown by merchant

• You don't need an aftermarket CPU cooler for these CPU's
• The cheaper monitor is likely similar quality, I would go for it
• I chose a slightly cheaper PSU and SSD that are still decent quality
• Slightly cheaper case that still fits everything you need
• If you can get the 1060 3GB for the price listed here the ~15% performance loss and 3GB VRAM is worth it for the cost savings. If you stretch the budget to ~$1,050 you can still grab the 6GB version