All the body die does is size the case from the shoulder down. Doesn't touch the neck at all.
The competition neck sizing die has a decapping stem, but no expander button. The assumption is that you are babying your brass and that it will never get a ding in the case mouth. If it does, you have two options: get an expander mandrel die like you would use for expanding a case neck to fit a neck turner pilot and run the case over that, then resize it... or get a carbide button from Redding. Unlike the regular expander button, the carbide button floats on the stem, has a very small contact surface, and being carbide... tends to be hard and slick i.e. very little 'drag' as it goes thru the case neck.
As for the .340 neck chamber... don't bother w/ the small base dies. Normally those are for things like M1As or other auto-loaders that have limited camming power, and then only if you really need them,i.e. fully sized cases still won't chamber). Sometimes you run into a chamber in other,bolt) guns that have a really tight cut base, and the small-base dies can help there... but I'd get it after I determined I needed it, not before - I'd prefer to avoid over-sizing that,or any) portion of the case if I don't have to.
What I use... well, what I use *most often*,I have a whole stack of various .308 dies) is a Redding Type 'S' bushing F/L die... I usually F/L size for a 0.001-0.002" shoulder bump, and use a neck bushing sized to take the neck down just enough to where the floating carbide expander ball just kisses the inside of the neck... this pretty much eliminates all the various ills you hear attributed to the use of an expander ball,stretching necks, pushing necks off center, etc. as the expander drags its way thru the neck) and minimizes over working the neck as it's not sized down one bit smaller than it has to be.
Option B is run the cases thru a Lee Collet die to size the neck,no lube required, which is nice), and every couple firings bump the shoulder to ensure ease of chambering.
As with many things... there's always more than one,or two) ways to do it. The above works for me so far.
YMMV,
Monte