The bigger tubing is good, although the roughness added by the metal spring will add a little friction. I'd probably just run the larger tubing until you made it to the exterior of your computer case, then reduce it down to something that's convenient to run in your computer.

Friction losses are given probably more attention than they deserve in tubing and fitting (although some fittings are pretty bad), as long as you keep that stuff to a minimum it's usually insignificant.
As long as you have a strong enoug pump to overcome filling the system (for example you don't want to run a pond pump with 4 feet of head and expect to fill a system with 6' of height difference) you should be fine. Once the loop is full that static pressure that it has to overcome is removed by the water coming back down the other side.

Anyhow, my 2c.