If you do actual submissions with various lenders, they will all have to check your credit. This is not good for your credit scores. That is your first potiental problem. When escrow is opened, it is ususally with the lender you choose. A title company can't open escrow with mulipal mortgage companies and issues title reports. If your loan is FHA only one case number can be issued. If an appraisal is ordered you will have to pay for all of the appraisals that are ordered. About $500 each. Many lenders will require you to give them your credit card info before they will do anything. They want your money upfront so they don't process a loan that will never close.
What you need to do to save yourself much effort and time, is to get good faith estimates from all of the lenders that you are looking at. All GFE's have the fees in different catagories. The 800 series catagory is for lender fees. Lender fees can not, by law, be anywhere else on the GFE. All of the other catagories will be the same for all lenders, title, escrow, home owners insurance etc. Add up all of the fees in the 800 series of each GFE and see who is the lowest. Once you have done that and you narrow down your search to decide who you will be working with, hang on to that GFE and take it to the closing and make sure none of the fees have changed with the lender you have selected. THe GFE is one of your best weapons against bait and switch. Beware of lenders stating that they have the lowest rates.
In addition to rates and fees, it would be an good idea to work with a lender who is local and you can visit face to face. An online lender doesn't care if you are "happy" or not. They want your money and the loan closed so they can move on to their next deal. A local lender has their local reputation to protect. Good luck