This is my first gaming PC build. AMD 3+ build for $500 take or give a few. Already have a HDD but if I buy one it would cost about $49.99. Getting all these parts from Newegg.com with promotion codes, other offers and shipping cost (Super Saver Free Shipping 5-7 days). Is this a good build?
Case: COOLER MASTER HAF 912 RC-912-KKN1 Black SECC/ ABS Plastic ATX Mid Tower Computer Case $39.99
Motherboard: ASUS M5A97 R2.0 AM3+ AMD 970 SATA 6Gb/s USB 3.0 ATX AMD Motherboard $85.99
The 4100 is, not so good, Bulldozer architecture. I would go with the 6300 (Piledriver). You don't absolutely need a full ATX board. You might need a new copy of windows if that is an OEM version (like from an HP, Dell, etc.). It will not activate on the new motherboard.
Yes, the i3 will beat the 4100 in every single way. Especially gaming. You could go with a fx-6300. I prefer Intel but that's just me. Its generally better as far as gaming is concerned but it's all personal preference.
The 6300 and the i3 3220 perform very similar in games. The i3 is much better at single threaded stuff while the 6300 is better at multi-threaded apps (because of the 6 cores). Either way, each build is good.