Move and rent out, live in & save for more rentals, sell

Ok so this is a long one, stay with me here, I could really use some advice. I will try to keep this as short and to the point as possible but heres the need to know info. Brace yourself for a couple follow up questions. I am a single guy in my early 30's and I've recently refinanced my house I am living in currently. I have the long term goal of financial independence with supplemental income from rentals. I currently do not have any rentals but would like to have a couple in 10 years or less. After my refinance, the numbers roughly work out to a savings of $450 a month and my mortgage now is just over $1k a month. My question is: should i live in the refinanced house that would allow me to save and invest the savings from the refinance ($450 a month) into mutual funds, orrrrrrr would it be better for me to move out, rent a cheaper place for myself, @ <$1000 a month? I can rent the house for around $1600 a month (side income of roughly $500 a month ($1600 rent - roughly $1k mortgage= roughly $500 a month). My If i rent, how much should I have as a security/home improvement fund for my rentals to cover unforseen expenses, missed rent, and repairs? Thank you guys for all your help