Well..... I lost my desktop in a house fire about a year ago. Somebody got distracted by his girlfriend and left a pan of Paella on the stove too long .
Wow, expensive dinner! So it appears you'll need a monitor and all peripherals in the mix?
For a cost-effective build that will get you all the bells and whistles with a 1080 p monitor I'd start with a 3 GB GTX 1060, 8 GB RAM, and the dual core i3 7100.
I expect some folks may weigh in in favor of a quad core cpu, and I would like to know what advantage a quad core would have for AH, especially for a low cost build, as I don't see need for it. When I monitor AH3 performance on my machine with MSI Afterburner, it looks like my GPU limits framerate when framerate dips below 74, and my i3 6100 CPU is not working nearly as hard to keep up.
And again you can find a similar level of compatible mobo etc. on the logicalincrements.com "very good" tier (the site is free btw, and only a resource you may find useful). To save $ consider leaving out the SSD, and go with the stock heat sink fan for the CPU, AH# seems to reply much more on the GPU. I find my GPU runs much hotter than the CPU running AH3.