1. If you want higher performance changing motherboard won't help, you need better CPU, RAM and GPU.
2. What about CPU for AM3+ MoBo, IMO for gaming best CPUs for low budget are Quad Core
AMD FX-4100 with 3.6GHz speed, 8MB l3 cache and Hexa Core
AMD FX-6300 with 3.5GHz speed, 8MB l3 cache, both support 1866MHz memory.
3. What about AM3+ MoBos, i would recommend ASUS mobos, because i'm using them about 10 years and they haven't failed yet. For those two CPUs, i would recommend these MoBo:
Asus M5A78L-M/USB3
It has 4 RAM slots (max 32GB) up to 2000MHz , USB3.0, onBoard
ATI Radeon™ HD 3000 GPU(if your dedicated GPU fails you can switch to onBoard GPU till you buy new one), also it has good feature called "Turbo Key",it allows you to easily overclock your CPU to boost performance and CrashFree BIOS 3 which lets you restore corrupted BIOS data from a USB flash disk containing the BIOS file.
IMO it is most optimal low budget MoBo for AM3+ socket with many good features.
4. What about RAM, it will be good if you use RAM with at least 1866MHz speed, because those FX CPUs support them, you can also buy RAM with 2000Mhz speed,because this MoBo supports it and overclock it to run at full speeds.
5. What about GPU for low budget gaming i would recommend
Radeon R7 260X from Sapphire \ Asus \ Gigabyte and
GTX 650 series from Asus \ Gigabyte (Battlefield 4 Ultra 25-30fps
😉 i own them, its my fps) or
Radeon R7 270 and
GTX 660 series (if you have more money to spend).
So the sum price of CPU + MoBo + GPU which were listed above will be somewhere 300-400$, IMO this is most optimal and budget FX build for gaming 😉