Plants that grow without CO₂
Start with plants that grow in low light: java fern, anubias, crypts, vallisneria, java moss and floating plants. Add a few fast growers such as hornwort or water sprite to use up nutrients while the slow plants settle. All plants by light need.
Light
Without added CO₂, extra light tends to feed algae more than plants. A basic planted LED on a timer for 6 to 8 hours a day is a common starting point for a low-tech tank; adjust from there by how the plants and algae respond. How to fit a planted light.
Nutrients
Fish waste feeds a lot of the plants' needs. Root feeders (swords, crypts) grow better with root tabs pushed into the substrate near them; stem and floating plants take much of theirs from the water, so a light all-in-one liquid fertilizer helps. Follow each product's label.
What to expect
Some leaves melt in the first weeks as plants grown above water in nurseries switch to underwater growth. A little algae is normal; a lot usually means the light is too strong or too long for the plants and nutrients you have. Identify algae.