You should secure the services of a buyer's agent, and let them know the school district you need to be in, and go from there. Let your agent know you realize you will have to make a slightly lower offer, but be willing to make concessions of your own, such as condition of the property, or not asking the sellers to make repairs, pay closing, etc.
You have received some great advice. The only thing I can suggest is to look for properties (with your Buyer's Agent) that have not been updated for many years. Their lack of modernization, means the Seller and his/her Agent should understand a reasonable offer.
I'm sure your Realtor will have some ideas on which properties are more likely to accept an offer in your affordability range. However, here are a few suggestions:
Look for properties that have been owned by the same person/couple for 10 years or more. Reason: If someone bought recently, they don't have much equity in the property. They might owe $160,000 and just hope to break even by selling for $180,000. You want someone who bought long enough ago that they owe approximately $130,000 or less. So you've got to go back aways.
Unfortunately, most of the properties I brought up in the $175,000-$200,000 price range in Gaithersburg are short sales. But there are a few bought a while back with plenty of equity.
Look for motivated sellers. That includes people who've had their homes on the market for a long time. That also includes people who are trying to sell a vacant house. It means they've moved but still have to pay the mortgage. There are a number of them that have been on the market for quite a while.
Also, be creative. Look for properties for rent. Have your agent approach the owners and ask if they'd be interested in selling instead. Sometimes people rent their properties because they figure it'd be too much hassle to sell, especially in today's market. Some of those would-be landlords would love to sell their properties.
Hope that helps.
However, Keep in mind that "the amount you can afford" will be the monthly payment..... The loan you can qualify for could be more or less than $150,000 depending on the interest rate.
Go make offers.. you can do this!