I was just thinking about this on the weekend. I fold off the line, my mum puts in a basket and brings inside to fold.
My method, as it saves sorting later, is wash things that get put away together in the same wash (dark/light dependent). When pegging, it is pegged by the drawer it's put away in - easy as that's how the loads are structured. Socks are paired as I peg. If I don't have the pair, I leave a gap for the second when it's found. If clothes go away on a hanger, they're not pegged they're straight on the hanger on the line.
Unpegging - unpeg, fold as walk back to the basket, place folded in basket by drawer (easy as that's how it's pegged), walk inside and it's super fast to put away.
Once you get the rhythm to hang like with like eg tshirts together, pants together etc it's really just pick the spot where it normally goes on the line and no thought needed.
My mum takes off line (hung in any old order), brings in, tips on bed, folds and sorts in to piles to be put away. Seems to take longer to me.
I don't iron until I'm wearing something. I prefer everything put away where it belongs, out of sight.