Conventional loans, like most loans are all about credit scores. Your middle FICO credit score must be at least 620-680. Scores above 720 rec'v. better rates.
There are conventional loans that allow as little as 3% down payment. All conventional loans obtained with less than 20% down will have a mortgage insurance premium added to the principal, interest, taxes and insurance numbers to calculate your monthly payment.
You can have the MIP removed later if the equity in your home goes above 20%
Rates are somewhere around the low 4% range, but obviously are changing all the time.