I think for very low drain devices like clocks, the advantage of better batteries like lithium starts to decrease. Alkalines perform pretty acceptably in very low drain scenarios. A lithium primary battery will still get more runtime than an alkaline in these devices, but the alkaline may get more runtime than an LSD cell. I believe under very light load, the capacity of an alkaline AA primary is around 2500mAh, but don't quote me on that, as I can't recall where I read it.
As far as which will cost you less in the long run, I'm not sure. Any battery that has a low self discharge rate should do fine for these devices (i.e. don't use non-LSD NiMH).
Also not sure about the remote scenario. I think a remote may draw a decent amount of power, albiet in very short bursts.