I think it's really important - they won't like it though and it won't mean you get to stop nagging but... If it's any help, this is what ours looks like with 3 kids and this has been in place for a couple of years so the youngest was 10 at the time. These are the expectations - they do other things as they crop up and like you, my eldest daughter is the star with doing things intuitively (though she can still dig her heels in when she's in a mood)
Daily chores - these cycle round, 1 responsibility each on a daily basis
1. Dishes (includes empty & stack dishwasher in the morning and dry and put away other dishes at night)
2. Take kitchen rubbish out at night and if it's rubbish night, the whole lot.
3. Take recycling out at night. Feed cat.
Weekly chores - these cycle round on a weekly basis and have to be done by a reasonable time on the weekend so it also means they have to take responsibility for organising when it's going to be done so that it fits in with other activities
1. Vacuum living areas
2. Vacuum and mop hard floors
3. Clean bathrooms
They are also responsible for their own bedrooms and the two older ones have to iron their own school shirts.
With the weekly chores, I wrote down what needed to be done and the kids made the decision on how it would be divided - we trialled it first for 3 weeks, then tweaked it a bit. They decided that even thought the hard floors was a big job, they preferred to divvy it up that way so they have a big job one weekend and an easy go the other times. It's not always up to the standard I would like, but unless it's really obvious that someone is slacking off, I let it go.