Cleaning a coffee machine that uses ground coffee is a messy, unavoidable chore. Paper filters are nice in that they can promptly be dropped into the compost -- as coffee grounds are extremely useful in the garden -- with a quick rinse to the filter basket, while gold-tone permanent filters do require a more rigorous cleaning.
Removable parts, like the brew basket, can be washed with soapy water and it's fine to wipe down machines with a damp cloth. On some machines, there may even be dishwasher-safe parts.
Typically, when it comes time to descale, your machine will let you know as well as detail their descaling process in the manual, which usually entails a descaling solution or vinegar mixed with water.
Tip: Invest in a pretty coffee canister to sit beside your machine, on your countertop, to make filling your machine a breeze each morning.