It doesn't matter whether you're down-sizing because the kids are all grown up and have left home or if you're looking at first time buyer mortgages, getting approved for a mortgage is exciting.
Checking into mortgages for first time buyers can be a risky thing and may affect your credit ratings. People often apply or check into online applications for cars, insurance and homes without knowing that their credit score can be affected (and quite often adversely). When you fill out online inquiries or applications searching for the lowest mortgage rates, the process can be deemed as an application by many companies. If your credit rating is low, you may be treated as a "rejection" which will show in your credit history. If you do this with several companies, your credit score can be destroyed without you even realizing the cause of your downfall.