Really for mine craft the computer doesn't need to be that powerful., If you start get high res textures and mods etc. You may need to. A really popular graphics card that could run even the highest textures well is the GTX 760. It really depends though. Make sure to look up tutorials on building computers to see what parts you need. You can also look at benchmarks to see which graphic card is enough to run the game. There's a channel on you tube called LinusTechTips have a look at that channel as they always look at graphics cards and compare them to other ones. Link will be in source.
Off of that now you will need a CPU and you need to find out what socket it uses so that you can get the correct motherboard for it. Then the other things are a Case to house the components in, RAM (easiest part to install), Hard Disk Drive (HDD), Power supply Unit (PSU), operating system and other parts are not essential such as optical drive, card reader but you may want them.
If you are at all intrested in buying a custom PC I'm trying to sell one and if you would prefer you can buy mine here is the link: http://www.gumtree.com/p/for-sale/custom-built-gaming-pc/1064344418
Hope I have helped you out.