You asked about tools and which scope mount.
A go-gauge looks like a stainless steel cartridge (with no neck) that is made to the standard chamber dimensions. It will chamber in a properly head=spaced firearm. A no-go gauge looks the same, but is longer, so it won't chamber in a properly head-spaced firearm. You don't really need a no-go gauge to install a barrel, as long as you have a go-gauge. You can put a piece of scotch tape on the head of the go-gauge and it should be really tight to close. It shouldn't chamber with 2 pieces of scotch tape on the head. Just a cheaper way to do the same thing as having both gauges.
Get a Barrel nut wrench and an action wrench to swap the barrels.
I have a Savage in 338Edge that wears a Nightforce 3.5x15x50 NXS scope. I use a DedNutz one piece mount and it works great, only $55 or so and is lightweight. Here is a picture.
Hope this helps,