CCI 200 and Remington 9 1/2 are standard Large Rifle primers which are pretty much interchangeable.  The brands vary a little bit in potency and cup thickness, but not significantly.  If you get a "magnum" large rifle primer like a CCI 250, they are significantly more potent.

As always, you should consider the standard disclaimer: if you are working near maximum loads, you should reduce the charge by 10% and work back up when changing brands of primers. 

But, in practical usage, standard large rifle primers are pretty much the same.

All the calibers you list will use large rifle sized primers.  You may want to use magnum primers in the 270 and 30-06 if using ball powders in very cold weather.  But right now you can't just go find primers on demand anywhere anyway, so use what you have.

Edited to add:  Remington doesn't make an 8 1/2.  They do have a 7 1/2, but it is a small rifle primer.  Won't fit in large primer pocket.