MSI GeForce GTX 970 GAMING 4G Video Card will it work with amd fx 4100

Yep.
Depends on the game so minimal with Tomb Raider but well over 40% drop vs a good i5/i7 CPU for some games.

So that does NOT mean you shouldn't buy the card just that you will have a CPU bottleneck for most games. Does that mean a GTX960 would be "better"? Not necessarily. You'll still get better performance in many games.

Some games would perform similarly with a GTX960 or GTX970.

*Another point is that DX12 games in the near future will significantly improve the performance of the FX-4300 and may reduce the CPU bottleneck completely.

That only works for DX12 games which means no game yet made; you also need to upgrade to Windows 10 which is free for W7/W8. We'll get more info once they start being released. I believe Microsoft claimed up to 50% more efficient, and additionally most games should use most of the four cores (so two different advantages; more core usage and more efficient coding).

DX12 games should take a while to come in so that may not affect your decision to buy a new PC.