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You have your sheet set up with 3 rows and 150 columns, correct?
If you switch to 3 columns with 151 rows (first row as a header row) your problem is easy to solve.
I have attached a workbook which shows this (add formatting to suit your tastes). It involves some simple steps handled by macros:
1) Data is entered on sheet1 ("Roster") ~ I added data validation in the "Comment" field to prevent misspelling.
2) Sheet2 ("Sorted Roster") requires no data entry - it refeences "Roster" to get all of the information.
3) On the "Roster" sheet the "UPDATE" 'button" (just a simple shape) has the macro "Up_Date" assigned to it. Clicking this does all the work.
4) After updating "Roster" data as needed, click the "UPDATE" button. This will: i) sort the data on the "Sorted Roster" sheet so all "Not Exempted rows are listed first; ii) pick a random row number for the rows with "Not Exempted"; iii) display the name from column "B" of that row in cell "F2" of the "Roster" sheet.
Hope you find this helpful.
Doug