For general biking around, a wicking inner layer is great. It doesn't haver to be a cycling jersey, wicking T shirts are fine, esp ones with a lower back hem.
The rear pockets can sometimes be useful, but if you wear them in layers during cooler weather, they can get uncomfortable. I prefer pocket-less inner layers. Long sleeve inner layers are also useful.
The difference in action between budget wicking shirts and big-name brands is not that much.