A high performance car has no place in a hyper-miler's garage.
If you understand that you will most likely spend more on piecing a bike together than buying a complete one and still want to do it for the experience then by all means. If you're doing it to save money - you will find that in fact you most likely will not save anything.
All of Shimano's groups have the ability to perform extremely well if properly installed and tuned. That said, I personally don't like any of the groups below 105 and I personally prefer ultegra or higher.
I have Tiagra from 2005 on my road triple. It runs great. My wife has much newer 10spd Tiagra on her compact, and its better again. If you're planning on racing and/or putting thousands of miles up or conquering Haute Categorie mountains, by all means go for the Ultegra or Dura-Ace, but if its for a commuter and you have a budget I say get the Tiagra and put the difference towards getting really good wheels or frame.
105 is considered pro level equipment though I doubt if you'll find any pros riding with it because it's a bit heavier. These days, 105 prolly performs about as well as Ultegra from a few years ago. As said above, it all works well if properly adjusted and maintained. Look for the deals out there, you may be able to find the upper end stuff for about the same price as the lower end if you shop around.