you should use a pressure washer, those can be found at rental shops or big box lumber yards. put a scoop of oxy clean in it. use a paint specific to vinyl siding, a dedicated paint store should have it.
Power wash so it’s clean let dry then paint with outdoor paint use a roller
First powerwash it with a bleach/water mix depending on how dirty it is use a 50/50 mix. Then the next day paint with resilience from Sherwin Williams i would highly recommend spraying the house but you can roll it also.
Green mildew easily washes off vinyl siding with a brush and dishwashing soap. Rinse with a hose. A pressure washer by itself won't touch it.
There is a special primer to use on vinyl. Check with Sherwinn williams. We did our shutters years ago and they still look great. No peeling.