I may be able to weigh in here, as I did a similar cemetery project a few years back.
It is not too difficult to use a python script to pass variables through to an SQL statement to select certain graves, but it can become very frustrating if you are unfamiliar with the syntax. It is a good idea to search this site for hints like Including variable in where clause of arcpy.Select_analysis()? and Multi Value User Input as Variable in SQL Statement
A relevant bit of advice in this situation is 'if you fail to plan, you plan to fail'. Will the graves be divided into several feature classes (as they appear to be in the TOC), or merged into one large feature? Will the user be able to select or enter multiple 'honors' for one individual? How much experience does the user have with ArcMap - will they be able to open the attribute table if more than one grave is selected?
Additionally, are you sure you want people to be able to manually enter something like "7th_Cav"? It may be easier to use a value list with preselected values. For example, you could have a parameter named 'rank', and select Filter > Value List in the Parameter Properties at the bottom of the Parameters tab to create a list that the user may choose from.
From my experience, it is easier in the long run if you limit what people can enter in the queries. It may initially be more difficult to setup and write a script, but can save you time overall.