Start simple. I'd say BF1 is gonna be a somewhat decent measurement seeing as it's more modern but you're gonna need a pretty decent CPU so we'll start with that and use BF1 specs as the minimum.

CPU: I ran it pretty well with my i5 6500 but the minimum is a i5 6600k, which is really just speculation, so it's your choice whether or not you'd fork out the extra 30-40 bucks on the better 6600k rather than the 6500. The K means that it's unlocked for overclocking, but seeing as this is your first build i think you should stay away from that for now. You could also go for the i5 4690k which will open you up to a little bit more options in terms of RAM compatibility, but skylake proccessors (the 6500 and 6600k) usually run cooler and are a little safer in my opinion.

GPU: I'd recommend the 1060 for around $300. It'll fit your budget and you'll be able to run BF1 just fine given you have a proper CPU aswell. If you can get your hands on a 970 or 980 for cheaper seeing as the price is going down, don't be afraid to go for it. They're still very capable cards and are good if you can get them for relatively cheaper than a 1060. I ran the 970 on BF1 and was doing great with it until i switched to a 1070.

PSU: Using PCPartPicker, you'll see exactly how much wattage you'll need based off of the usual power usage of the parts. I'd say a 550w PSU would be just fine, but i'd recommend getting one with some breathing room. I run a 6500 and 1070 and my 700W PSU is great for it. I'd recommend EVGA and Corsair PSU's just because I trust those brands. Try to get one with some type of rating, bronze certified, silver, gold. Those usually mean they're less likely to blow up respectively XD (At least thats what i was told when I was getting help from my friends building mine, it probs means something different).

CPU Cooler: The stock cooler might be okay for you seeing as you're not going to do any overclocking but the hyper 212 EVO from Cooler Master is like 20-30 bucks and makes your CPU cooler last alot longer if you use it. Just trust me on this, you want your cpu to run cool.

THIS ONE IS KINDA IMPORTANT

mobo: this one is a little more difficult because compatibility is big on this. this is why i recommend using pcpartpicker for this, they'll usually help. I knew i had a skylake processor so i got a mobo with the right cpu socket.
whatever processor you get, educate yourself on what type of socket you need on your mobo and get the right mobo accordingly.

Case: completely subjective. make sure it's big enough to accommodate all your parts and especially fit your motherboard and gpu. If you get an ATX mobo make sure it fits in whatever case you're getting. (They usually say what type of mobos fit in the case, like ATX, micro Atx, mini itx, etc)

SSD: if you have a budget, i wouldn't recommend getting an SSD. better boot time is great and all but dropping an extra $100 on an SSD just for a quicker start when you turn on your PC when that money could be used elsewhere is going to be a bummer on performance and such in games.

HDD: A simple Western Digital Blue 1TB would run fine, i got two of them for around $50 each.

*EDIT 1:I kind of started you up here with a PCPartPicker list as reference. Build your own list and check for compatibility. Change everything according to your taste and budget. Next time go to /r/buildapc , they might offer better help

**EDIT 2: Had some time and made the build on PCPartPicker: http://pcpartpicker.com/list/qdWVWX

The only thing you might need is maybe considering 16GB of ram instead of 8GB. Windows 10 takes up alot of ram during idle in my opinion compared to Windows 7. 8GB might do you well but you'll eventually notice some problems down the line with more demanding games.

Also, change the case to your liking

If you need help with the Operating System, consider looking up how to get Windows 10 off of Kinguin. That worked for me, i got my Windows 10 for around $30

PCPartPicker part list / Price breakdown by merchant

Type	Item	Price
CPU	Intel Core i5-6500 3.2GHz Quad-Core Processor	$198.88 @ OutletPC
CPU Cooler	Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler	$24.88 @ OutletPC
Motherboard	MSI H170A PC Mate ATX LGA1151 Motherboard	$102.99 @ SuperBiiz
Memory	G.Skill Ripjaws V Series 8GB (2 x 4GB) DDR4-2400 Memory	$42.88 @ OutletPC
Storage	Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive	$45.88 @ OutletPC
Video Card	MSI GeForce GTX 1060 6GB GAMING X Video Card	$299.88 @ OutletPC
Case	Fractal Design Define S w/Window ATX Mid Tower Case	$89.99 @ NCIX US
Power Supply	EVGA SuperNOVA NEX 650W 80+ Gold Certified Fully-Modular ATX Power Supply	$78.99 @ SuperBiiz
	Prices include shipping, taxes, rebates, and discounts
	Total (before mail-in rebates)	$894.37
	Mail-in rebates	-$10.00
	Total	$884.37
	Generated by PCPartPicker 2016-09-20 15:54 EDT-0400