My storage process is:
I have everything in soft-sleeves as a standard. I top-load any autographed or memorabilia cards as a standard practice. Then for anything else, if it's book value of $5 or more, it gets top-loaded.
I keep rookies / prospect cards in binders based on the birth year of the player. I keep those stored together per year so that when a group reaches 30 years old, I can bundle them and get rid of the no-namers. The list of guys who became something notable that late in their career arc is really slim.
All the insert / parallel cards get put in binders by year / brand / subset.
All the standard base cards get grouped by star name in binders.
Any thing left after that (the base no-name players) get put in boxes by year/brand at the moment. I'm trying to figure out if it's easier to bundle them up by year/brand or by team-lots to get rid of.