[Laserminer]

I have a pretty cool opportunity where my friend wants me to build a budget PC. He will use it for Minecraft, less graphics intensive games, music playing, internet, and making Minecraft videos.

Budget: $500 USD at most.
Parts not needed (already has them): Monitor, keyboard & mouse, OS

For Minecraft he wants at least 40fps, usually 50-60. Brand of processor/gpu does not matter, only performance for price and not overheating. For Minecraft do I need to get more than 4GB memory? Is integrated APU okay? Which are more important - Processor, Memory, and/or GPU? Please use your current desktop setup as examples if useful.

[TechnoProdigy]

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($119.99 @ NCIX US)
Motherboard: ASRock H77M Micro ATX LGA1155 Motherboard ($75.66 @ Newegg)
Memory: Corsair XMS3 8GB (2 x 4GB) DDR3-1333 Memory ($54.99 @ Microcenter)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ Outlet PC)
Video Card: PowerColor Radeon HD 7770 GHz Edition 1GB Video Card ($99.98 @ Newegg)
Case: NZXT Source 210 (White) ATX Mid Tower Case ($39.99 @ Amazon)
Power Supply: Corsair Builder 500W 80 PLUS Bronze Certified ATX12V Power Supply ($47.99 @ Microcenter)
Total: $498.58
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-06-15 16:56 EDT-0400)

This should do the trick.

[Laserminer]

The computer will also run servers sometimes; is this build alright for that?

Also I've heard processor is important for Minecraft. Is this i3 okay even though it's fast?

[TechnoProdigy]

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Amazon)
Motherboard: ASRock 970 Extreme3 ATX AM3+ Motherboard ($84.99 @ Newegg)
Memory: Corsair XMS3 8GB (2 x 4GB) DDR3-1333 Memory ($59.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ Outlet PC)
Video Card: PowerColor Radeon HD 7770 GHz Edition 1GB Video Card ($99.98 @ Newegg)
Case: NZXT Source 210 (White) ATX Mid Tower Case ($39.99 @ Amazon)
Power Supply: Corsair Builder 500W 80 PLUS Bronze Certified ATX12V Power Supply ($57.74 @ Amazon)
Total: $522.66
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-06-15 20:16 EDT-0400)

This build will probably be a bit better for Minecraft and running a server, however it's slightly over-budget.

[Laserminer]

Thanks for picking parts! However, I don't know about the processor, but he wants occasional LAN servers not a big one (Idk about 6 cores...)

--> Where is a fan or cooling system though? It can't overheat (then I think it lags). Also the hard drive can be 500 or 750GB after these changes it should be good

[TechnoProdigy]

Thanks for picking parts! However, I don't know about the processor, but he wants occasional LAN servers not a big one (Idk about 6 cores...)

--> Where is a fan or cooling system though? It can't overheat (then I think it lags). Also the hard drive can be 500 or 750GB after these changes it should be good

The case comes with enough fans and the stock cooler should be fine. I'll edit this and add an aftermarket cooler.