Hi @Nadir M.,
Congrats on closing on your first rental!
I would keep it simple and do the first and late after the 3rd. But some people like to collect rent on the day of the month that the property is leased from (ex. Tenants move in on the 15th - you collect rent ever 15th of the month). I think doing it on the 1st is the simplest.
Definitely post your ad on those two sites. Zillow will then go and post your ad on to Hotpads and Trulia for you. You should be able to find someone to rent it from one of those sites. Also if you have the chance to go out to the property it would be a good idea to put a sign in the yard. Do you plan on being out there during the leasing process? Someone will need to show the property to prospective tenants.
I have a property out of state and I use a property manager. They list the property, do all the showings, do the background checks, write up a lease, collect the rent for me, and handle maintenance issues. It makes things easy for me because I don't have to worry about chasing a tenant down if they don't pay rent. Or if something breaks down, I don't have to find a contractor to fix it. I was also a property manager for 3+ years - so I like using them and can see the benefits from them.
Hope this helps! I'm happy to answer any other questions.