I am not sure about the shaders, my 7850 even doesn't cut above 30. There is yet an official/proper testing on it. But, According to people here:
http://www.minecraftsurvivalgames.com/threads/shaders-mod-requirements.61432/
You at least need around 960/285 performance cards, and that could add up to $200 alone. You have only $100-$150 to spend left on other parts. That equates to very cheap parts that is very hard to squeeze in. My best try is:
http://pcpartpicker.com/p/7cKqQ7
If this is what you're looking for I think you're good. But I won't build it this way as it probably would not be a good build (as it is not balanced). Unless that '350' is Poundsterling or Kuwaiti dinar or something like that I think it's hard to build anything. But if you're playing without shaders, It's very easy. I built an AMD richland rig only for ~$220 back 2 years ago and it runs minecraft fine.