Nice barn !

Are other elements of the barn going to be stained / painted as well?

Shiny / glossy finishes are generally not found with stains. If that is the look that you are after then you are most likely into paints. that said Sansin does make a product that might work. https://www.sansin.com/product/ens/

But in that location I would look at paints first.

Thanks! I plan on staining the posts as well. Also, there will be wooden windows and barn doors all over the barn that will also be stained. I am wanting, at a minimum, a satin look to all of the wood trim. The doors and windows will be made of ash, not pine. Do you know if I need to condition the wood first?

This always depends on the stain that you end up using. Each manufacturer has different application requirements for raw wood applications. Check the labels first or ask where you are purchasing the product.

Thank you for the advice. Unfortunately, I am having all of my barn doors and windows made by the Amish in my community. Don't get me wrong, I think they will be absolutely beautiful when completed. But, the Amish guy making them doesn't have any advice as to stain and such. With such an expensive order to boot, I sure do not want to mess them up.

Then go to a local paint store - not HOME DEPOT - and ask a professional there. You might even consider taking them to a millwork company / cabinet maker and have them professionally finished.