You have 20 days to request a hearing. A hearing date is usually set about 45 days after arrest. An attorney needs time to obtain evidence and investigate defenses. You should probably make a decision on who to hire within 30 days at the most.
The sooner you can retain an experienced DUI attorney the better. There are a number of things your attorney will be able to have you do proactively in order to improve your situation, and the odds the case can be resolved without a DUI conviction or all the other consequences.
The DOL hearing has to take place within 60 days of your arrest, but your attorney is able to continue the hearing in order to be fully prepared.
The sooner you hire an attorney the better. But, you don't have to hire an attorney to request a DOL hearing. You must request the hearing within 20 days or you waive your right to a hearing. However, you could request the hearing and then hire an attorney before the hearing is scheduled.