Mine attempt to make their own beds and help sort laundry out. Every week they tidy up their bookshelves, bedroom toys etc. They also "help" set the table, clear dishes away, and clear up bath toys after their bath. I am extremely lax about tv, I don't really set limits, my children are 7,5 and 2.
To be honest the rule that has worked best for us - is just that they are nice to each other, everything else just seems a lot easier if they aren't bickering and winding each other up.
I'd make a list together of what they can do, given their ages, and what they will do to help.
3 yr old: tidy toys away, get dressed, put dirty clothes in dirty laundry, do the dusting (his choice), help with hoovering (his choice again and really bloody annoying for me as he just plays) Put lids on pends and tidy pens and crayons away.
6 yr old: tidy up after himself, clear his and brothers plates, get dressed, brush teeth and wash face, put dirty clothes in dirty laundry, keep his desk tidy, put books away, put his and his brother's clean clothes away. Help me load washing machine/dishwasher. Empty dishwasher and washing machine. Help dh or myself wash car. He does some of this, some of the time without nagging .
my 5 yr old helps set the table, returns his plate and cutlery to sink, helps empty dishwasher, dresses own bed (ie pulls up duvet ) puts dirty clorths in laundry tidies playroom after being asked 20 times
my 3 yr old - same but with even more mess slightly less aplomb
my 2yo and 5yo both have to put their toys away in the evening, put their clothes in the laundry basket, clear the table after meals, "help" wipe up any spills they make, help set the table, and put their own rubbish in the bin.
it's really not a lot, just a few one-minute things, but i think it helps to get across the idea that mummy is not a servant as early as possible