Properties do not always reduce in price. Unless the house is listed in a declining market, I usually do not recommend sellers keep reducing their price until it sells. But, ultimately it depends on the urgency of the seller. You can negotiate a lower purchase price is the seller is willing.
The others are right that your first step should be in finding what you can qualify for. You can check online calculators for how much you can afford, but these only tell you part of the picture. A qualified lender can give you a free quote over the phone on what interest rate you might be able to get. They will likely need to pull your credit to make sure, since this is a main factor in determining your rate.
Best of luck!