As to whether a player should walk ...

With each team having a limited number of appeals available, it makes sense to stand your ground. If not given 'out' (possibly because it was a 'no ball') then the opposition have to consider using up one of their appeals. If given 'out' (and you think there's any room for doubt) then your team may consider using up one of their appeals.
If you know for certain that you should have been out then you can choose whether to walk before, or after, an appeal. Your team captain may have his own view on your decision!