Hi there.
I'm personally going to be starting an aquarium with live plants in the near future and have been doing some research.
Tha main benefit is that the plants will add oxygen to the water for your fish while the fish will give the plants the carbon dioxide they need. And plants shouldn't cloud your water and if they do it might be because of algea, not the plants you've put in.
The problem with plants though is to be careful when selecting them because certain ones require a lot of light to grow properly and lots of light might mean lots of algea in your tank. Check out some of the sights on line that deal with aquarium plants. I have been having a hard time finding a good one, but they will at least tell you the strength of light different types of plants require.
Also, if you're starting from scratch (just starting the tank) you might want to consider placing peat plates under the stones for the roots to dig into and provide the plants with more nutrients to grow. And the peat is supposed to be good for the fish too. These plates should be at your LFS if not ask for them.
I hope this helps some.
And if anyone has anything else to add, I would greatly appreciate it too.