Adding house wrap behind existing board and batten siding
If you are going to do this you might as well go all the way.  The housewrap is kind of like saying you are cold so you put on some underwear.   Might warm you up a little but being fully clothed is what you want.   

If you are taking the siding off you should be throwing up (at least) 1" XPS rigid sheets.   I prefer to put the housewrap up first and then the sheets.   You tape the joints on each.   

After that the only three issues are getting the old siding up, making sure you have enough siding up, and extending the trim around the windows.   


Remove siding.   
Caulk and spray foam gaps, especially near windows.
Add housewrap and tape.   Note this will not take away all air movement.   
Add 2" XPS (1" is fine).   With you and two teenagers this is a 4-5 hour job - it cuts with utility knife and really only windows take any time.   Get peg nails and tape.  In the corners you put up 2x4 plus 1/2" plywood.   Your house will be 4" longer.   Cut out right to windows and doors.
Add blocking plus trim around windows and doors to match new house depth (this is a different question and way easier than you think.
Add siding back on.   Like I said you will need an extra 4" per side.  That is why I asked if you have extra siding.


The housewrap is nominal.   There is no way in hell I am taking off all of my siding to just housewrap.   Adding insulation is a long-term investment in the house.   In heating and cooling in southern IL (I am near you) you will pay for the extra costs in probably a year.