First, go read the MSAA, SSAA and FXAA wikis.
FXAA/MLAA are basically the same thing. They are shader-based and therefore really cheap to implement in terms of processing time. Good FXAA will give you 90% of the image enhancement of 4x MSAA, at a much lower bandwidth cost.
SSAA basically renders the image at a multiple of the display resolution then samples down from this. Excellent quality, but super-expensive to implement.
MSAA is more brute-force than FXAA, but it's effect is also more accurate. It's less accurate than SSAA, but cheaper. It also has the negative of not having any effect in the case of deferred shaders, as the MSAA pass happens before the post-processing pass. So, best? There isn't a best. Both have there negatives.
In PC gaming, here's my recommendation: Aim for 60fps. Once you've achieved that with your settings, then think about AA. If you are running something like a Geforce 650 at 1080p, then take FXAA when you can, otherwise forget about AA except on older games. A 660 or higher lets you run 4xMSAA or higher, usually with some FXAA on top of that. Moving from 30 to 60fps screen update will have a greater effect on your experience than any AA style will, so target that first.
On my Radeon 6870, I hit 60fps pretty regularly. In older games I tend to slap 2xMSAA on top of that. I can't recall anything that I've played that offers FXAA. Maybe Deus Ex, in which case I went ahead and used FXAA instead of MSAA.