Re: zeiss conquest 3x9x40 - 270 or 7mm08
Welcome to the forum! In my opinion, long action vs short action doesn't have much to do with scope selection (at least directly).
Typically, the scope will be matched to the purpose of the rifle:
xxx- A lightweight scope on a mountain or carry rifle.
xxx- A heavy, higher-mag scope on a heavy, dedicated long range rifle.
xxx- A low-mag scope on a rig used at shorter range.
Because you already have your scope chosen, I would pick caliber based on your preferred ballistics (and what type of shooting you are going to do).
I don't have a 270, but it is an established, flat-shooting cartridge that lots of folks swear by. There are a lot of options in factory ammo, but bullet selection is somewhat limited if you reload (relative to other bullet diameters, but by no means is it rare). I do have a 7-08, and think it is a great, low recoil deer caliber. There are lots of 7mm bullets to choose from if you reload, and factory ammo is available (maybe less premium stuff than 270?).
Let us know what type of hunting and shooting you plan on doing, and I'll bet you get some opinions on these two calibers (and probably some others)!