Welcome to the Planted tank as a member. Heavily plants will help jump start the cycling process. Plants help break down toxins and use it as a food source. The more plants you have the better the natural filtration. Plants are your best filter bar none. Heavily planted can vary for many. Some may consider heavily plants as no visible substrate. Some look at it as just being very dense but clearly the substrate can be seen. Others may look at it as being so populated that you can't put any more plants in.
As far as I know you have stem plants and you have rooted plants, you can also throw floating plants in there. Most stems will take from the water column better vs rooted plants take from the substrate better. Some stem grow roots from nodes. A good mix can get you the best of both worlds. Depending on your setup, heavily rooted plant can get your planted more established. Especially if you use the dry start method. Once your tank is establish to combat algae you can always swap your plants. But starting with heavily toxin eating plants will get your tank going in no time.