What are the minumum and maximum requirements to play minecraft on PC?

If you want to play the game without too much lag then 2-4GB of RAM at about 1333MHz will suit you fine. You will need a graphics card of at least 512MB preferably with active cooling. 8GB of RAM and a 2GB video card will Minecraft at max settings with Max FPS and no LAG.

Well I had the lowest of low - AMD A4 5300 @3.4ghz, 4gb ram and an AMD 6450 card, that ran everything on good settings while recording. A PC like that will only cost you about £300 or $500

Minimum Requirements:
•CPU: Intel Pentium D or AMD Athlon 64 (K8) 2.6 GHz
•RAM: 2GB
•GPU (Integrated): Intel HD Graphics or AMD (formerly ATI) Radeon HD Graphics with OpenGL 2.1
•GPU (Discrete): Nvidia GeForce 9600 GT or AMD Radeon HD 2400 with OpenGL 3.1
•HDD: At least 200MB for Game Core and Other Files
•Java 6 Release 45

Recommended Requirements:
•CPU: Intel Core i3 or AMD Athlon II (K10) 2.8 GHz
•RAM: 4GB
•GPU: GeForce 2xx Series or AMD Radeon HD 5xxx Series (Excluding Integrated Chipsets) with OpenGL 3.3
•HDD: 1GB
•Latest release of Java 7 from java.com

Software Requirements:
•Minecraft Release 1.6 or newer. Older versions will need to be updated to current versions
•Please note that some users experience issues playing Minecraft while using a mismatched version of Java for their operating system (32 or 64 bit), while using certain versions of Java 7, or while multiple versions of Java are installed

64gb RAM
i7 4960x Extreme core
4x GTX 780ti Quad Sli
ASUS Rampage IV Extreme

Should do the trick.