There are a few breeds that lay (almost) every day and many breeds that go broody a lot but they aren't the same breed.
2 reasons for that. Breeds that have been developed to be daily layers have also been selected NOT to go broody.
If they go broody a lot they wouldn't lay every day because they take a couple months off when they're broody.
There are other options. Get good laying breeds and a couple birds of a broody nature to set on the others' eggs.
Or get good laying breeds that also tend to go broody.
Breeds that tend to go broody can have individuals that never go broody, good laying breeds can have individuals that like to brood. I had a Black Leghorn(good laying non broody breed) hen that raised 4 clutches for me.
Orpingtons, Penedesencas, Delawares, Hollands, Langshans, Sussex, Australorps and Fayoumis lay well and tend to go broody. The latter two will be in the over 200 egg a year group.
Of the breeds that lay 200-300 eggs a year, it's a gamble that you will get a broody in the bunch. Those would be Leghorns, Anconas, Minorcas, Jaerhons, Rhode Island Reds, Dominiques, Hamburgs.