You can pre-qualify with anyone you want but that doesn't mean they have to actually lend you the money. You need to get pre-approved and that you only want to do with one company. What you CAN and should do is call around and find out how much they charge in closing costs/fees for a house at a certain price and then find out the current interest rate, although that changes daily. This way you can compare apples to apples on say a $300,000 house or what ever price you use (use something that you realistically might spend on a house).
Keep in mind that your regular bank may be the best source especially since you may qualify for other perks with having a mortgage with them (free safe deposit boxes, interest on checking and savings accounts, no service fees, free ATM's, etc.).