You can use regular milk in your DeLonghi Magnifica S for cappuccino. For the best froth with small bubbles, skim or 2% milk works best, and it has to be cold—straight from the fridge. Whole milk will froth, but it might not get as thick and microfoamy.
If you're getting disappointing results with your regular milk, try a different brand before you blame the machine. Some milks just don't hold air well. Non-dairy milks are hit-or-miss and can be an experiment.
Clean the cappuccino maker nozzle after every single use. Milk residue is the number one killer of good foam.