What gaming PC shall I get for minecraft?

I have a budget of £800 and would like to get a gaming PC that can get me at least 60fps or over. This includes whilst recording with fraps or no that it stays at 60 or goes over. I'm mainly gonna get this PC for minecraft, since I have a yt channel based on it. Please refer to me the cheapest you can find, although as I said my budget is 800.

Any pc with iCore 5 or higher like 7.

Here are some great specs:

Intel i5 3570K or AMD 8350 (Both are great but i prefer amd)
500GB HDD
550W Corsair PSU
Asus motherboard for around 90$
MSI r9 270x gaming edition
8GB corsair vengeance 1600mhz ram
Corsair carbide 300r casing

http://www.palicomp.co.uk/gaming-pcs/INTEL-Haswell-i5-Commander.html
INTEL Haswell Core i5 4670K (Quad)
Overclocked To 4Ghz Per Core
ASUS Z87-K
CRUCIAL BALLISTIX 8GB 1600Mhz
KINGSTON 60GB SSD SATA3, 6Gb/s
SEAGATE 1TB HDD SATA3, 6Gb/s
SAMSUNG 24X DVD+/-RW
AMD Radeon R9 270X 2GB

http://www.palicomp.co.uk/gaming-pcs/alpha-fury.html
INTEL Haswell Core i5 4670K (Quad)
Overclocked To 4.4Ghz Per Core
ASUS Z87-K
CRUCIAL BALLISTIX 8GB 1600Mhz
SEAGATE 1TB SATA3, 6Gb/s
SAMSUNG 24XDVDRW
AMD Radeon R9 270X 2GB
ASUS 24'' VS247H LED HDMI HD TFT Monitor

http://www.palicomp.co.uk/gaming-pcs/excalibur-core6-watch-dogs.html
AMD Vishera FX-8350 @ 4.0Ghz (8 Core)
ASUS M5A78L-M/USB3
CRUCIAL BALLISTIX 16GB 1600Mhz
SEAGATE 2TB SATA3, 6Gb/s
SAMSUNG 24X DVD+/-RW
NVIDIA GeForce GTX760 2GB
FREE GAME - WATCH DOGS

http://www.palicomp.co.uk/gaming-pcs/eyefinity-slayer-lite.html

AMD Bulldozer FX-4130 @ 3.8Ghz (Quad)
ASUS M5A78L-M/USB3
CRUCIAL BALLISTIX 16GB 1600Mhz
SEAGATE 1TB SATA3, 6Gb/s
SAMSUNG 24X DVD+/-RW
AMD Radeon HD7770 1GB & Eyefinity Adaptor
3 X ACER 22'' LED HD TFTs
3 FREE GAMES - Farcry 2, Deus Ex & Dirt3

http://www.ukgamingcomputers.co.uk/the-block-minecraft-gaming-pc-p-160.html

Streaming will add strain to the CPU so upgrade the CPU to one of the i5 options then save the rest and go down the pub with it. Absolutely Zero reason to spend any more.