There are plants which grow with their roots in the substrate, plants which are grown attached to decor and plants which float on the surface of the water.
The plants grown in decor include those which have a rhizome which must be above the substrate so the safest way to stop it get buried is to attach these plants to decor; and also mosses which don't have roots. These are usually slow growing plants which require little in the way of fertiliser, maybe just a small dose of liquid fertiliser. Plants like all the mosses, Java fern (several varieties now available), anubias (several species from tiny to huge), bucephalandra (many available in different colours and leaf shapes), and plants like Bolbitis.
Floating plants range from the tiny invasive duckweed, through salvinia, red root floater, frogbit, water lettuce up to water sprite. With 60 litres, you may find water sprite plants a bit on the large side. Floating plants have two uses - they give the fish a 'roof' over their heads sheltering them from bright light and potential predators (they don't know there aren't any); and they take up a lot of ammonia from the water.
Plants rooted in the substrate range from easy, low light plants such as cryptocorynes and sword plants to delicate, high light loving plants. As a beginner with planted tanks, I would stay with the 'easy' ones at the start. Some plants are leaf feeders which need liquid fertiliser added to the water; others are root feeders which need tablet fertiliser (root tabs) inserted into the substrate near the roots.
Aquascaping has become a big thing with plants treated almost as an art form. But you don't have to go in for 'scaping, the fish will be just as happy with a tank with lots of plants which wouldn't win prizes for artistic design. I am hopeless at 'scaping, I just put small plants at the front and tall plants at the back
Other members will be able to help with layouts if this is what you would prefer.
This website is useful for plant research. You can search by difficulty which I find useful. They also have photos of tanks using each plant so you can see what they look like when they have settled in and are growing well.
The right aquarium plants
tropica.com