I've tried the basket system, looked for lid holders (too expensive)

finally decided the best way to store is with the lids on. saves
later frustration. This will also identify lids with no partners, ergo
you can reduce lid clutter (bottom clutter too)
they don't nest well, they tend to stick or get wedged in too tight,
and it's a pain and time waster to put them away in proper nesting
order.

sorry, I can't resist- stationERy, when you mean papER, stationAry
when you mean plAce.