Once you have figured out how much cash you could raise for a down payment, you should have an estimate of how much you can spend for a home. Use 20% as your starting point.
If you have $30,000 to put down, divide that by 20%. This will give you $150,000 as an answer. If this seems reasonable for a home in your area, you have the whole spectrum of loans from which to choose. If this is unrealistic for your area, you know that you are going to need a loan with less than 20% down. If you divide $30,000 by 10%, you get $300,000. Is this realistic? Play with the numbers.
The greater the percentage you can put down, the more loans are available to you. You should also include a cushion of a few percent for possible points and closing costs. You are also going to need moving money, and you do not want to move in without some money for unexpected expenses.