I have issues with the different pans, and am trying to generally get away from non-stick as well.
I've found with some practice that the same rules apply to the stainless steel (and the ubiquitous aluminum in commercial kitchens) fry and saute pans as do to the cast iron or the anodized (my fave 12" pan).
I don't use soap unless I've been cooking something acidic or fishy, fairly rare. I wipe or pour out excess fats (
not in the sink drain, plays havoc with plumbing, septic and sewers, y'all!), and store. IF I had to use soap or for that matter sand, I clean thoroughly, and reseason. Yes, the other pans as well. Mostly, I leave them, if already seasoned, with a very thin film of the current cooking fat on them, whatever doesn't easily wipe out.
And when cooking,
always preheat the pan then add the fats/oils. It gets into the pores and the pan is less likely to stick. Most foods, you need to leave them long enough to actually caramelize on the bottom before moving or turning, they tend to release themselves when that happens. Schmaltz or any kind of fowl fat
is excellent. Coconut oil or clean pork/bacon fat is excellent. The saturates seem to work best, though high smoke point oils are very good, too.
This is helping me quite a bit with the whole sticking problem...the big test being eggs over easy, without breaking!