easy (not necessarily cheap) plants for bettas tanks are java fern, java moss, and anubias (not anubis - he is a god). All will grow attached to driftwood or stone so are easy to move around, and are tolerant of low light. hornwart is also good, and just floats like a soft green mass in the tank (ie, you don't plant it). They don't need CO2.
Carpet plants are not so good unless you have more light. I am not that well up on high light plants so will defer to the opinions of others. Higher light can only be utilised effectively by plants with adequate CO2.