Because of the complexity of immigration law, sometimes requests are denied and must be appealed. If you work out a flat rate with your attorney, be sure in advance that your appeal is included in the rate they've quoted. You don't want an unpleasant surprise later on.
Is your immigration law attorney a specialist in a particular type of immigration law? If so, make sure they specialize in at least some of the aspects of your case. If you're in need of asylum, you don't want someone who specializes in obtaining work visas.