Rather than develop his own record keeping application he would probably be better off purchasing an already developed system from one of the numerous medical record system vendors. He'll get a better application and have people he can call on for support. Plus there are all of the legal issues about medical record storage and access. A vendor will have worked out those problems already.
That having been said there are many other file based databased systems out there: http://www.google.com/search?q=file+based+database
I haven't used any of them so I can't make a recommendation.
Of course, there's always the various enterprise databases (Oracle, MySQL, SQL Server, etc...) as well. Of those SQL Server is probably the easiest to learn for a newbie. Since there's no 64 bit version of Access I'm starting to see people replace Access with SQL Server Express (free!) for small applications that need to run on 64 bit windows.