Having one breed that supplies that is going to involve keeping a LOT of birds.
You want good layers, for eggs for eating and hatching. Good layers usually aren't that meaty, and they don't go broody.
If you want broody hens to hatch their own eggs, you have a hen out of egg production for about 2 months.
Large, meaty birds don't lay many eggs.
Have you eaten a dual purpose cockerel? They're quite different than a grocery store chicken, both in size and texture.
My advice it to start small, with enough layers for egg production. Plan on 1-2 hens per person, depending on how many eggs you eat. A production bred hen will usually lay 6 eggs per week her first laying year, so that gives you a starting point. If you get pullet chicks this fall, you'll raise them up and have eggs incoming in the spring. At that point you'll have a few months of chicken husbandry under your belt and can add more birds in the spring. Along the way, if you get an Oops cockerel, butcher it and see how you like it. In the spring, you can get some straight run birds and raise the cockerels up and butcher them. Decide who you like, to keep as a breeder. Purchase an incubator and start incubating and hatching eggs. Grow your numbers as your space, time, etc allows. Don't expect to jump right into having a complete self-sustaining flock, it's a process that can take a few years to find the right mix for you.
another option is to simply raise batches of Cornish cross for the freezer. I don't know how much freezer space you have, but doing 50 of those birds gives you a nice amount of meat. Plus, they're over and done in 8 weeks. Raising dual purpose cockerels for the table, you've got to take them to around 20 weeks for a meal. Some folks butcher as young as 13-14 weeks, but at that age there's very little actual meat for a family meal. You've got to house all those males somewhere, and dual purpose cockerels have pretty poor feed conversion rates compared to meat birds. Free ranging and buying feed in bulk will help, but over time you're going to spend more on them than you would on a batch of CX.