Pat,
I generally use rounded tees, but make sure the "bow of the boat" as I call it points the right direction. It seems to help alignment challenged golfers like you, even though there is no rule that I must do that.
Agree rounded tees just naturally fit rounded land forms, not to mention being more practical for most to mow. Even when I use rectangles, they have small rounded edges, maybe 8" Radius so the mowers don't have to pick up on the clean up pass. Some, not all, superintendents find that sort of a waste of time for a specific look.
I recall visiting the RTJ II office many years ago. The subject came up, and their take was rectangles made sense as "form follows function" unless there was a dramatic natural land form or tree you wanted to work around. Of course, they were from the runway tee school of thought.
BTW, I'm not 100% sure any course has to have all of one or the other. Nothing wrong with an eclectic mix of rectangles on flat ground, round ones fitting slopes, etc. Even free form tees, a la, Larry Packard and Innisbrook are very nice, little pieces of art.