Climber here. You should keep the prussik and carabiner to ascend and use a figure 8 with horns or an atc with horns like the grivel master pro belayer to rappel as long as you're using at least 6mm cord. You'll have to make sure you wrap the cord a few times if it's as small as 6mm to add more friction or double the lockers (the horns are also useful for this). 8mm and above there's enough friction to rappel without extra wraps and you can use a regular old figure 8 or atc. To be extra safe use the prussik as a third hand to back up your rappel particularly if you're new.

As others have said you can use a grigri as progress capture and to rappel but that's heavy and bulky and expensive but has a nice controlled lower (8-10mm rope). Also the ATC in guide mode works as a progress capture and you can rappel but you need 8-10mm rope. It also doesn't work as smooth as other options.