I just looked up at mortgage and that is about $1100 a month on 235K for 30 years.
Your $3000 will cover the closing costs (title insurance, etc.)
I would also recommend to save cash for at least the first 2 months of being vacant, though you put vacancy into your calculation, if you are vacant the first month, you are out $1700 right out of the gate...and you don't want to accept the first renter that comes through the door, be careful who you rent to. Depending on the house age, I think the $100 might be either right or too low for maintenance/capex costs.
I would actually recommend if you are 24 (especially if you are single), do a house hack with it (live in part of it and rent out other rooms to people). Buy it with mortgage of $1700 (after all ins and taxes, etc) as a primary residence, and rent out parts of the house. You will reduce your living expenses, do some improvements as you live there and bring the value up, plus you will eliminate your own rental expense....so you can probably live there for free, depending on the number of bedrooms, etc.
In a year, you can re-finance it or rent it out as a whole or move out or whatever else that may work, while at the same time you will build equity in it on someone else's dime.
Just my 2 cents.