I make my living as a house painter. ( So I know a little about latex/oil paints) Latex paint will be easier to use
BUT........
Test the old paint on the barn, You cannot put latex over oil paint!!!!!
If you do the latex will peel probably within the year.
The way you test it is to take some denatured alcohol ( rubbing alcohol )
Put some on a rag and rub a fairly clean spot of old paint on your barn, then look at the rag, if the color of the barn has rubbed off onto the rag the old paint on the barn is latex.
IF.....
If no paint rubs off onto the rag, the barn is painted with oil.
To put laten paint over the old oil paint you would have to apply a full primer coat before the latex finish coat .
Now you can use a latex primer or oil primer over the old oil paint it really doesn't matter if the primer is oil or latex.
Also, if there is any bare wood, from peeling paint or new wood, you should also prime these areas.
Also, if you are sanding down any areas on the barn,WEAR A RESPORATOR. Old paint has lead in it and can possible cause some health problems. But I beleive they took a lead out of house paints in 1978 or 79. The top layer of paint may fall into those years or later but if you have an old barn theother layer of paint may contain lead, better safe than sorry!!
This post is kinda long, ( Sorry ) but didn't want you to put all the labor into your barn and have any problems later.
P.S. Just a little plug, I am in St. Clair/ Union Missouri area, just out of St. Louis. If anyone needs a painter in St. Louis area, let me know.
( Would this be consider SPAM LOL)
Good luck with your barn