There is a strategy section for threads like this, just to make sure you have a wider range of opinion.
Short stacked games play preflop and on the flop but rarely further.
Speculative hands have little place in your opening < or worse, calling range >. Less true if the table folds post flop - but then you could effectively play any two cards as a bluff. Pretty suited connectors are no good in a short stack environment.
Yes, play premium hands. Noting that "premium" means a rather wide range at a four player table. Basically you should be playing "top pair hands", generally aggressively.
Normally calling aggression preflop is a mistake. If you can't 3-bet, then you should be folding. The SPR is going to be low - top pair rules the roost.
How you proceed post flop depends on the table. There are times where a 100% c-bet strategy can work out. But mostly you can thrive playing to make top pair and checking if you miss. Be sure to press your luck when you flop a big draw. There is a lot to be said for showing down some semi-bluffs to get action when you have top pair.
This can be a high variance environment, but also a high win rate game as well. Be prepared to go bust several times and even so go to war the next time you have a top pair hand.
By the way - it is perfectly rational for a weaker player to buy in short. Better by far to play four $75 buy-in vs a single $300 buy in if you think you might a soft spot.