For that type of usage and budget, you probably want 32GB of RAM, at least DDR4-3200, which will cost about $350 at current prices for decent Samsung B-Die RAM (good compatibility with Intel and AMD). So count on that eating that portion of your budget whichever you go with, or about double that amount if you want to go for 64GB (doable within your total budget, depending on what parts you pick). Faster RAM will benefit games and applications, but you'll want to check what's been verified to work depending on what motherboard you get, as beyond 2666/2667 is technically overclocked (though sanctioned by XMP/AMP on both Intel and AMD platforms).
You'll be going with current high-end consumer rather than HEDT (Intel's Skylake/Kaby Lake "X" X299 lines, AMD's Threadripper) because of the higher price and power requirements of HEDT. So that means deciding instead between Coffee Lake i7 and Ryzen 7.
Coffee Lake i7 will be better for gaming, while Ryzen 7 will narrowly be better in some to most workstation/professional (multithreaded) workloads, at least at stock. If you are overclocking, the i7-8700K is more tempting, but will be harder to cool and use more power. If you aren't overclocking and you decide to go with AMD, go for the 1800X - otherwise the 1700 is cheaper and will can OC to 3.8-4GHz; the 1800X is just binned slightly better (meaning you may get an extra 100-200MHz more), and has a higher guaranteed base clock.
I can't tell you to go with Intel at the moment unless you can find an i7-8700K (or 8700, if you aren't overclocking) in stock. Availability is low across the board, and while stores may get resupplied, they may be hard to find until next year. If you can find one, though, then that would be my recommendation. Coffee Lake with 6 cores is a much better proposition for professional uses (video encoding, 3D rendering, VMs/servers, etc) than Kaby Lake was, while costing minimally more and being even better for games thanks to higher clock speed.
As far as motherboards go, for AMD the ASRock Taichi is one of the better X370 boards (at least last time I checked), though personally I'm fond of my ASUS Crosshair VI Hero. There are less expensive boards, though, it's just a matter of what features and style you want. AMD has committed to supporting and releasing new processors for AM4 until at least 2019... Intel may not support Z370 for beyond Coffee Lake.
For an Intel Z370 motherboard I don't know if there are enough reviews yet to make a clear recommendation, but ASRock, ASUS, Gigabyte, and MSI all have decent looking motherboards out right now, and frankly I haven't seen much reason to pick one company over another as far as reliability over the past few years.
ASRock has become a favorite of many lately, though, and I do agree they have good features, build quality, and support (from what I've heard, haven't had to use it yet, so that's a good sign), so they might be worth considering. Both their Taichi and Fatal1ty lines are excellent for either AMD or Intel. I have an ASRock ITX mobo coming in tomorrow for an i7-8700, so we'll see how that goes.
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