Try them out for yourself. TXAA should be good against shimmering, but rather blurry compared to MSAA. FXAA is not all that great in itself, but it doesn't affect performance as much as the other modes and can often be combined with eg. MSAA for a very good result (apart from some blurring).
SSAA almost always gives the highest picture quality, but it is much more demanding than the other modes, so only use it if it doesn't murder your FPS.