I agree chores are part of living in the house and don't get paid for (different if they are "above and beyond" type things e.g. we paid DS for painting the fence).
We explained to our teens that we expected everyone to pitch in as we all lived here. We suggested tasks but also asked for their input, so we have their agreement that this is fair. As I have 2 children that watch like hawks for any sense of unfairness, we also made them "equal".
They agreed that one would lay the table and wipe down afterwards. And they picked days based on clubs etc. DH and I graciously agreed to do the 7th day :)
Everyone puts their plate etc in the dishwasher after dinner.
They both cook (at your ages, I think we started with prepping dinner first and progressed to cooking with support) one day a week. The person cooking also leaves the kitchen afterwards. They agreed which day they wanted but can swap if they let me know in advance.
On a weekend we all pitch in and do a house clean. I tried to introduce a rota but it caused too much aggro, so we now have it that DS hoovers and dusts upstairs and the stairs, and DD does the downstairs. DH and I do the rest. We don't define when they must do their hoovering, so they fit round their social plans.
Their own rooms they are responsible for. We have made threats (thankfully not carried out), regarding keeping them at least at a basic hygienic state.
They change and wash their own bedding and towels. (I think this might have started later than 13).
I wash their clothes but they iron anything they want ironing. Surprisingly, they don't usually bother :)
I would say that we've always had jobs since they were toddlers, so it wasn't a huge shock. I can see implementing for the first time might be harder. We do point out how much we do for them that we don't have to, that makes their lives nicer (lifts was a big one).
We allow leeway/no jobs around exam/busy times.