So many plants offered for sale are not true aquatic plants. It is always safe to ask a fish retailer which ones are best. Some grow better and faster than others without much use for fertilizers and CO2. We recommend both of these treatments for healthy plants but understand that many aquarists choose to do without.
A couple of our favourites are the many anubias varieties and java fern. Both do well with little effort. An air stone will remove much of the necessary CO2 from the water so if you are trying to grow live plants and you want extra oxygen, then maybe a power head is a better way to go. Lowering the water level when using an "over the top" mechanical filter is another way to increase your oxygen.
Always cut their roots back to 2” or so before planting. Remember that some fish love to eat plants. Be aware of the type of fish you have. Silk and plastic plants may be more for you.
If you find that you are getting an increase of thick green algae on your plants, then you could be over feeding flakes or that you have too many phosphates in your food source. A really great pleco can clean this up easily. It also could be a problem stemming back to that air stone that you chose to leave in.
Try not to move the live plants around to often. They will really flourish if they can establish themselves in one spot.