Julie, I have made staging and also made the basic mistake of under estimating how heavy trays of grit with plant pots full of soil and plants can be (and I am an engineer), my first effort many years ago slowly collapsed with everything on it as I was at the opposite end of the green house to the door, it took a while to clear space to get out as it was partially propped up by large pots on the other side.
In this green house I have two stagings against the wall I made, and two aluminium stagings I can remove when winter turns to the tomato season on the other side.
Having some old four by four fence posts, I made a good top frame resting on four solids legs then braced the back and side legs, across the top having some 2x1 wood cut it into batons and lay it across the top frame screwing some of them down, in my case I also screwed the top to the wall which with your greenhouse you will not be able to do, So two home made stagings, I split them in case I want one out and built a sand box with heating cables on one of them, that is heavy although has not moved in the years it has been there. You do not brace the front as you store things under the stage.
Four good solid legs
A good frame on top
Brace the back and sides
Then use your pallet flats for the top
Put a small pave under each leg to stop it sinking into the ground.