Congrats on starting out!
My husband and I started our property management business about 18 months ago and absolutely love the service and peace of mind we are able to provide to clients.
Percentage of income is often how people charge but this varies widely by location and also type of rental. With short term rentals, you tend to take a larger cut as there are many things involved in the day to day upkeep, think 12-25%. With long term rentals, the comision is a little smaller think 7 - 12%
Can't speak too much on placement fees from personal experience as we focus more on short term rentals in our business, but I have seen many people charge them... rightfully so. It takes a lot of work to find a tenant, your commision gained from the income should only be for the services rendered while the tenant is in the home ( in my opinion ).
Some additional fees I can think off, are maintenances fees, for larger projects that require a lot of management and research. Also eviction fees, because that is NOT an easy or fun process to endure.
I hope that helps!