A system that can play Minecraft on Fancy like I play it on, well just to let you know that it may be done. Using lower CPU and GPU since my computer's 6150SE has issues running Minecraft on low settings with 64bit JAVA.
The only time I can run Minecraft flat out is with my XFX 5770 but you may be able to suffice with a 3870 or lesser GPU. For $250 I'd have to suggest a refurbished PC. Just ignore those HP DC7700's with the x1900/1550 GPU because it fails to run minecraft because of legacy drivers.
Minecraft system requirement's.
Any computer with the following hardware should suffice, however, for an enjoyable experience, we suggest looking at the Recommended Requirements.
Minimum Requirements :
CPU : Intel P4/NetBurst Architecture or its AMD Equivalent (AMD K7)
RAM : 256MB
GPU : ATI Rage or GeForce 256 with OpenGL 1.2 Support
HDD : At least 90MB for Game Core and Sound Files
Java Runtime Environment (JRE) 6 and up is required to be able to run the game.
Recommended Requirements :
CPU : Core2 Duo or AMD Athlon 64 (K8) 2.6GHz
RAM : 1GB
GPU : GeForce 66xx or ATI Radeon 9xxx and Up with OpenGL 2 Support (Excluding Integrated Chipsets)
HDD : 150MB
The system requirements are not really extreme, but please remember that Minecraft is extremely JAVA heavy. Just opened mine in the back ground to monitor it, already consuming 50% CPU and 800MB's memory on highest settings with my guy sitting in his little house on top of a mountain. Already hitting 900MB's of memory. Just playing around it consumes around 35% of my 5770's processing power and is sitting around 1GB of memory used, DDR2 800.
What OS are you running, you just simply mentioned Windows?