I'm in favor of the monogrammed shirt, especially a polo-type, or something with a collar.
T-shirts with the barn/ranch/club logo aren't bad, but they do tend to look more casual, like something you'd buy as a souvenier at the gift shop. A shirt with a collar looks a little more professional, and there are plenty of horse catalogs that offer monogrammed products.
When I ride, I typically just wear jeans (I like my Wranglers at the moment), Ariat paddock boots, sometimes chaps, and a t-shirt or some kind of button-down shirt in hot weather. In cooler weather, I layer up. Long sleeve t-shirt with a vest, polarfleece pullover or zip-up, etc.
In rainy weather, I wear an oilskin coat or my lightweight outback coat that rolls up and zips into its own pocket for easy packing.
"Parelli horsemanship is just like painting by the numbers. You need absolutely no skill. You just put this color here and this color there, and when you're done, you have ... a mess no one wants." mp