Fertilizers yes, but not CO2, depending.
An established tank can have sufficient natural nutrients for plants, but this depends upon the plant species and numbers, fish load, feeding, etc. I have had tanks where no fertilizer was used, but other tanks need some. If adding fertilizer, it is best to add a complete or comprehensive supplement so everything is being supplied. This can be risky if one goes about it individually, adding this and that mineral/nutrient. Plants need 17 nutrients and in rough proportion to each other. Some nutrients can be stored, but not by all plants. So excess nutrients can cause issues, not only algae but some plants may shut down assimilation of certain nutrients if there is an excess of another nutrient beyond their capacity. That is a very complex subject, but the point is that using a comprehensive supplement is the best and safest way. The nutrients must also be in balance with the light intensity, or again algae can take over. But both light and nutrients must be sufficient for the plants, and no more (or less).
I use Seachem's Flourish Comprehensive Supplement for the Planted Aquarium, and another near-identical product is Brightwell Aquatics' FlorinMulti. I also dose a new tank to give the plants a start when natural nutrients are absent (until fish begin adding them). Long-term, some tanks get a regular weekly dose, some not, depending upon the response of the plants. We must remember that every substance added to the water in the aquarium does get inside the fish, in the bloodstream and internal organs. So keeping all additives minimal will always mean healthier fish that are not being possibly weakened by this or that.
Which brings me to the CO2. Are you planning on diffused CO2? The plants mentioned earlier do not need this. There is often sufficient natural CO2 if the tank is a low-tech or natural planted method aquarium. Most of the CO2 comes from the breakdown of organics in the substrate, and then from respiration of fish, plants and some bacteria.
