I am glad you found someone although I was hoping you would have more than two choices. If you are anywhere near a large City then there should be more than two med mal attorneys. As far as the fee goes, you should review the contract carefully. Some provide for a 1/3 fee if the case settles before suit, then a greater fee after suit is filed. Some firms charge more if the case goes to trial. 40% is actually common in lots of places if a lawsuit is filed and the case goes to trial. Don't be afraid to ask this attorney for references or about cases he has tried. Some things may be confidential but many may be public record.
FYI, there are other types of malpractice. Attorneys get sued for professional malpractice too. Lots of other professionals such as accountants, architects, etc. may be liable for doing work that is substandard. You don't hear as much about these cases in the news because medical mishaps are, unfortunately, more newsworthy.
Good Luck! R