College App Help/Resources

A relative of mine was badly hurt in a commercial vehicle accident and now we are trying to understand how attorney referral actually works before we agree to anything. How do you usually verify that a referral service sends your case to a lawyer who really handles that specific type of claim and not just to whoever is free that week? I came across one site where construction accidents, pedestrian cases, fractures and slip and fall claims are listed as separate practice areas and it made me wonder how much detail is realistic to expect before the first conversation. What weighs more in your experience, the list of practice areas or the actual case history behind it. I would also like to understand how the no upfront cost arrangement is normally explained, because that is the part I follow the least. For now we are just comparing a few options and reading the terms slowly.