Credit can vary from excellent to a recent bankruptcy.
Your rate increases the poorer your credit is but the loan can still be done. I have many different lenders with many different programs and rates. Appraisal, Title, Escrow, Tax Service, Recording and Flood are the main 3rd party costs. In fact, I typically only require a small deposit for the credit report and appraisal up front and that is credited back to you at the close. I typically can have an official lender approval 3-4 days maximum from the time the application is submitted.