Is a tourist visa or a fiance visa the best way for a legal alien to enter the states to marry a US citizen when they have been engaged and been seeing each other frequently for the past 3 years?

I would say a tourist visa (6 month) is best because a fiance visa limits your time and is not one that can be renewed like a tourist visa. You can renew a tourist visa for 6 months. It does not always get approved but it is something that is possible with the tourist and not with the fiance visa. Now if you plan on getting married as stated in the fiance visa then in that case this would be the one for you.

United States Citizenship and Immigration Services, http://www.uscis.gov