Any advice as to storing starched fabrics?

Same as non-starched fabrics.

The only problem with starched fabrics is if you live in an area where starch attracts bugs -- primarily hot, humid climates. Starch is an organic product -- comes from potatoes, rice, corn, etc. -- which is why bugs can be attracted to it.

Please try to get a climate controlled unit...my girlfriend didn't. She had a dresser that had been her grandmothers in there, as it didn't fit in the apartment. The heat in the unit curled the paint and dried out the glue in the joints.
Some of the things she had stored in plastic bins did not fair well in the heat.

Do not get the "giant" plastic totes - get smaller ones that can be picked up and stacked easily. Also, do not get the cheaper ones whose lids just snap on - pay a little bit more to get a tote that has a handle that actually is the lock on each side of the tote. Also, I found it easier to tell what was in each one if it was clear and not a solid color.

My BFF passed away several years ago and had a massive stash - it covered several rooms in the house and the basement. Imagine my shock when we stopped in to see her DH and he said he had spent the past two days burning her stash. I thought I was going to be sick. She had a sister and a daughter-in-law, a granddaughter and many nieces. Anyway, I rescued all of the fabric, etc. that was in the bedrooms - he wanted it "gone" in a hurry, so my DH and I ran to WalMart and bought many of the huge totes and filled them up - when my DH went to pick them up, they were so heavy that the snap-on lids just snapped off. So, we had to unload them all and take them back to WalMart and get smaller ones that had handles that were part of the lids. A much better idea. They have "grooves" on the lids so that they are very "stackable". They are the "Sterlite" brand at WalMart - but I am sure there are other brands at other stores.