https://pcpartpicker.com/user/bluescreen1985/saved/C7G8TW (Nvidia) https://pcpartpicker.com/user/bluescreen1985/saved/WGhbt6 (AMD) If your budget is $800 you can upgrade the i5-6400 to a 6500.
First link is a good all round PC, i5-6400 and GTX 970. Should run almost anything in 1080p high/ultra 60fps. This is an improved version, still within $800, with a faster CPU and better motherboard. This is assuming you already have a monitor and peripherals. If you don't, here's a part list for $600: http://pcpartpicker.com/user/bluescreen1985/saved/WgFV3C The remaining $200 should be enough for a good monitor and keyboard/mouse.
Then go with the $600 build. You can find a good 1080p monitor for $100-150, you can get a decent kb/m for $50. It's not as powerful, but still a great PC that will run most games on high settings 1080p at a stable 60fps. You could get a GTX 960 instead, but you shouldn't - the R9 380 is a better card for the same price.
http://pcpartpicker.com/user/bluescreen1985/saved/WgFV3C he just gave you the link - this is the $600 one so you can buy monitor, keyboard and whatnot
It's far too subjective to recommend keyboards or mice. Some people insist on mechanical keyboards, others (like me) don't care in the least bit. You need to find a good keyboard and mouse for you yourself. When it comes down to monitors, I can recommend a BenQ GL2460HM - it's 1080p, good colours and response times, has HDMI and speakers, and is fairly cheap.
Just a heads up, mechanical keyboards are expensive. Like $80+ for the low end boards. I absolutely recommend buying one if you can afford it, but never prioritise it over a better PC. If you want a cheap and really good mechanical keyboard, check out Unicomp. They make Buckling Spring keyboards starting at $84. No fancy RGB backlight or media keys, just a really good keyboard with really good switches you won't find anywhere else. It's basically an IBM Model M, built in this century - the design remains unchanged for good reasons.
If you must have a mech and want one thats cheap I could suggest this one.. Found it a while ago and was thinking of buying one myself. Its not MX Switch board but its a mech. http://world.tmall.com/item/521328073753.html?skuId=3106218801182
Price in $/£? Honestly I wouldn't trust some Chinese board, I'd rather spend more and get a Unicomp keyboard - it's cheaper than most MX boards, and built to the specification of a Model M, so expect it to last for 30+ years.
Those builds are perfect! About the monitor: get a second hand IPS monitor from a 'good' brand, possibly with warranty. I'm currently using a Dell P2414H. 1080p and IPS display, which means excellent color reproduction and viewing angles. Very satisfied. TN displays generally have a bit lower input lag, but suffer from narrow viewing angles and more 'washed out' colours.
About 24$ and I never said it was going to be a great board just saying its a mech and its cheap. Also if you are up for reading more on the board. https://www.reddit.com/r/Mechanical...d_up_the_keyboard_that_was_selling_for_20usd/
Honestly, I wouldn't buy it. But it's your choice. I prefer to stick to trusted brands myself, even if it means buying a lower end product or spending more.