You should always search based on the price of the home. You would have received a maximum mortgage amount at the time of the approval. Remember that your approved payment amount will also include your property taxes and homeowners insurance. Between that and the down payment factored into the theoretical payment appearing on Zillow, shopping by payment will only get you into trouble.
While I agree with @TTrumble for those who are not good at numbers, I myself have put together a plan to find a house, where I would first look at the properties I like, then figure out the price, then figure out the monthly mortgage (P+I only) and add monthly taxes and insurance (PITI). If this amount is higher than my monthly limits, I would then consider if buydown can cut that PI part (you can’t do anything about the TI part) so that the PITI can come within my reach (which is <31% of monthly income). Of course one needs sufficient funds for buydown, but one can arrange it by “gifts”/”loans” from family members or tapping into retirement accounts without any penalties. After all this if the home is not in my reach, I would move on and find the next one. When I closed, my options were limited (I was a non-priority member, so I had to look only into priority areas), but now that one can purchase a house anywhere (just learned about it today from @Nelsont and @TTrumble), a sweet problem to have is to factor in the interest rate (1% higher rate in non-priority areas for non-priority members – whatever terms NACA is using for it! The site surely can have some help with up-to-date and clear information)
@pratik There must have been a misunderstanding or miscommunication, because non-priority members are still not allowed to purchase in an MSA greater than 100%, unless it has been determined to be a high cost of living area.
@justapproved_22. I would utilize a mortgage calculator to determine if the property will fit into your approved monthly payment. You can adjust the down payment to zero or just use the mortgage calculator on NACA.com.