Stefanie, I've been using Apartments.com (Previously Cozy) for more than 10 years. It is completely free for the landlord and tenants and the site makes money through premium features like background checks, speedier processing of rent payments, etc.
I can post rentals, accept applications, do background checks, create leases and send them out for e-signature all for free. It's an awesome platform.
The site also allows tenants to pay with ACH for free or for a fee, the tenant can pay with a credit card.
I use all of the services above, but the Expense Tracking service, also free, is an invaluable resource for my property management. It puts each expense in the appropriate IRS code and punches out year end summaries that I email to my tax team.
You can also have tenants submit repair requests through the site but I don't use that as I have good relationships with all of my tenants.
I can't recommend Apartments.com more. Good luck!