At one year, I am not sure if they have had an adult molt yet or not. Some pullets don't have an adult molt their first fall and winter but keep laying all winter. Some do molt, however. Why that is important is that chicken egg production stays about the same after the first adult molt as before, but the egg size and quality tends to improve. After the second adult molt, which may be this coming fall or the following, egg production on average drops by about 15% or 20%. After every adult molt after that, egg production will drop another 15 to 20% on average. For commercial operations, that drop becomes enough that they are better off replacing their layers pretty often. With us, especially if they free range and find a lot of their own food, that drop off is often not as important.
Each and every chicken is different. Some drop in production more than this and some less. You have to have enough chickens for the averages to mean something. It sounds like you are planning only two or three. You may get one that is not near the average, either way, so your results may be off the average. And this is drop in production, not total production. It depends how much they lay to start with. Some hens of any breed lay more often than others to start with.
I'd suggest a minimum of three. They are social animals and need to have other chickens around. If you only get two and something happens to one, then you have a problem. If you have three and something happens to one, you have time to solve the problem.
With the one year olds, you should get pretty good egg production this year whether they have already had an adult molt or not. They may lay as well or even better next year. But after that, you will probably notice a drop-off.
Starting with year olds means you will need to replace them or get some new ones to add to them a year sooner than you would have if you had started with chicks. One big advantage is that you know these are hens. If you get chicks, you might get a rooster.
I've had Delaware and Black Australorp. I think they are both good choices.