Formula for you
=ArrayFormula(IF(C2:C="Current",INDEX(SORT({COUNTIFS(INDEX(SORT({C2:C,ROW(C2:C)},2,0),0,1),"Current",ROW(C2:C),"<="&ROW(C2:C)),ROW(C2:C)},1,0),0,1),""))

Edit: Include more than one label
=ArrayFormula(IF((C2:C="Full-time")+(C2:C="Part-time")+(C2:C="Contract"),COUNTIFS((C2:C="Full-time")+(C2:C="Part-time")+(C2:C="Contract"),1,ROW(C2:C),">="&ROW(C2:C)),))
or
=ArrayFormula(IF((C2:C="Full-time")+(C2:C="Part-time")+(C2:C="Contract"),COUNTIFS((C2:C="Full-time")+(C2:C="Part-time")+(C2:C="Contract"),">0",ROW(C2:C),">="&ROW(C2:C)),))
or
=ArrayFormula(IF(ISNUMBER(MATCH(C2:C,{"Full-time","Part-time","Contract"},0)),COUNTIFS(MATCH(C2:C,{"Full-time","Part-time","Contract"},0),">0",ROW(C2:C),">="&ROW(C2:C)),))
or
=ArrayFormula(IF(ISNUMBER(SEARCH(C2:C,"Full-time"&"Part-time"&"Contract"))*(C2:C<>""),COUNTIFS(SEARCH(C2:C,"Full-time"&"Part-time"&"Contract")*(C2:C<>""),">0",ROW(C2:C),">="&ROW(C2:C)),))

Function References