Look, you do not need a dedi- video card. A good list of specs are...... (see below)
8GB of DDR3 RAM (Random Access Memory) OR MORE
Anywhere above 500GB of HDD (Hard Disk Drive Aka hArd Drive)
I prefer an Intel Processor. i3, i5, or i7, really. As long as it is about 2.6-2.7 GHz and above.
It is alright if the processor includes a GPU (Graphics Processing Unit aka Graphics Card) An Intel HD Graphics 3000-5000 (something like that) should work. it will last longer and be able to play more games if you get a dedi- graphics card, such as an AMD FX, or an NVdia Gfx card.
Atleast 15'' screen, which is the usual size
I reccomend Hewlett Packards, but a dell would do just fine. Do not hesitate to ask a professional. You can go to a place like Best Buy, or TigerDirect, and they can tell you more about what is optimum for gaming. (They may not know Minecraft. Ask about GMING IN GENERAL if you do.)
-Carter