Full, multirow panorama

I’ve been banging my head over this issue for a while now, so I decided to ask here.

I need to create a full 360 degree panorama suitable for mapping onto a sphere or cube for a custom VR application. It needs to be fairly fast to set up, because I want each panorama as a frame in a video

In case I didn’t make what I want to do clear enough, I’ve already tried making a standard panorama (but those images were too big and I never found the right camera settings to avoid a fisheye effect), and I’ve tried render baking a perfectly reflective sphere (but for obvious reasons that had too much distortion).

If this is impossible, or if it’s absurdly easy, or if my question still isn’t clear enough, my sincere apologies for wasting time and server space.

Apparently my question was either stupid or impossible (and I sure hope the latter).
Ok, I’ll revise it:
What value should I use for my camera lens setting if I want to have a square 90 degree FoV shot suitable for something like a Quicktime VR?