Wouldn't three locks get a bit heavy, especially for a long commute? If you lock up to the same place every day, maybe get permission from the owner there to be able to leave a heavy duty chain lock (true
security chain, not the chain cut to at Gnome Depot) on the rack. This way, you can carry a U-lock and be able to lock up most places, but at your destination, you have both locks as protection.
To minimize the issue of people stealing components and such, if your ride is something you will be commuting with on a daily basis for a while, I'd consider locking skewers, or at least Allen head or Torx bolts for the wheels and seatpost. This way, you can just lock the frame and not worry about your wheels being missing when you return. You can also lasso a steel cable through your stuff, but because it is so easy to cut those, it provides no more than token protection.
I wonder if you would be better off, instead of three locks, you might look at one Sold Secure Gold lock, and a set of Pitlocks that cover the seatpost, both wheels, the stem, and the brake bolts (either rim or disc). This way, you can just focus on locking your frame to a sturdy object and calling it done.