Your opening post is correct: live plants are a wonderful thing both for fish and for you as the viewer, but they do need to be healthy and flourishing and therein lies the trick, when they begin to turn yellow and brown, for whatever reason, they are adding to the ammonia load on the tank and can obviously then place an additional bioload on the filter.
I agree that vallis can often be included in the list of good beginner plants but darn(
! ) anwhyte, you forget that vallis is only "easy" for you people with hard water! For those of us with very soft, acid water, vallis can take a heck of a lot of patience!
I also agree with the startoff list there of Java Fern, Anubias sp., certain Crypt sp. and we could add Java Moss and some sword plants (although always check on whether they might get too big for your tank) and there are pretty many others if you do searches here on TFF for "easy plants." There is also at least one list of "easy" plants in George Farmers post over in planted. The term "easy" refers to plants that are slow growing and don't need particularly special conditions. Slow growing plants of this sort often will thrive with "low-light" technique where the light is down around 1 watt per gallon extra CO2 is not provided and even the plant nutrition may be limited to the fish and plant waste in the tank, although often these are supplemented, especially in a new tank that may be too "sterile" for plants to survive.
I do often recommend to beginners that they be cautious about investing in more expensive plants during a fishless cycle as the ammonia situation (assuming there's light too) can lead to algae getting a grip on the plant leaves, which can be frustrating if your budget was tight and you hoped these plants would last on past the fishless cycle to be part of your aquascape. On the other hand it should be realized that peoples conditions vary widely and its also quite common for people to find that many plants absolutely thrive in their tanks with great ease, so it can be a wonderful thing and little worry, you just have to find out!
~~waterdrop~~