Natural plants are better for fish under most circumstances. The negative circumstances really only come when the plants are dying... fouling the water. Beyond that they help to regulate the water chemistry, keeping the dangerous nitrogenous waste byproducts of the fish down... a mini ecosystem really!
Another case of plants and fish not mixing is African cichlids and plants... they just destroy them. Adding some easy to grow plants to your tank adds a wonderful dimension and another whole layer of learning. Plants are fun to research and try out. The key is matching your plants to your lighting. Everything else can be tweaked here and there. Generally simple ones like java fern, anubias and many cryptocorynes require very little effort on the part of the first time aquatic gardeners, though the crypts do appreciate a bit of root fertilizer every few months,
