It is important to maintain a bank account in good standing. Keeping your account with a positive balance is a good way to build your credit standing.
If you do not have a bank account you should definately obtain one. Look for one that gives you a good percentage rate so that the money you are saving can grow more rapidly. Anything that can help your money grow is a good thing.
One thing mortgage lenders like to see is that you have been able to have saved some money. Try making some amount of deposit monthly to grow your balance.
Money is not always needed for a down payment, but there are almost always closing costs, unless the seller has agreed to pay them.
