LOC is the first one to be pressed just because it is the first one to be captured, however if you already captured GS you may press APP first because APP it's LOC & GS in one...

The reason why pilots may choose to press LOC and APP individually its due the fact of certain situations, one may need or want to perform a particular path prior engaging LOC or APP for good approach reasons.

300 VS will not break your air plane but it's not the most comfortable landing for sure, and if that is the best you can get with an autoland it means something still needs the company attention, in this case the Captain Sim attention.  I had experiences with the aircraft performing a dive of death while on autoland to correct it's descent rate, and therefore no time at all to flare.. in fact only time to crash.