I have been summoned!!!!

hehehe
OK, first and foremost - this is like a chinese fast food menu. You have a column of wants, you only get two.

Seriously, modern man has purpose built birds to do one thing really, really well. Getting a bird that does several things well is something of a Holy Grail, many
quest for it.
So, here goes -
1) Prolific Egg Laying - the best birds for this are the various Sex Links (red sex link, black sex link), which are all hybrids, and won't breed true. Of the two, the red sex links are the best, because they tend to be smaller (less feed consumption) yet produce similar sized eggs. Sold under various names (Comets, Cinnamon Queens, ISA Browns, Amberlinks, etc). These are also famed for reproductive problems, early - often year three, sometimes sooner, rarely later. They are called sex linked because they can be identified immediately as male/female at hatching, males are quickly culled.
**DON'T PANIC** Many old "Dual purpose" breeds (understanding that the expectations fo 30, 50, 100 years ago are radically different from the expectations of today - we've been spoiled) have been preserved by commercial breeders and hatcheries - and since they make their money selling chicks, those DP birds have been selected for egg production (while any pretense at fast growing meatiness has often been a secondary concern, at best). They will, however, breed true - for good or ill, largely passing down good egg laying and not much else to write home about.
2.) Meaty Beast - Absolutely NOTHING compares with a CornishX, a purpose built (orignally hybrid) now bred from specialized lines. They grow incredibly fast (to the point of endangering their health), have a huge breast (and therefore, white meat) to leg/thigh ratio compared to most all birds, and do it with incredible efficiency. This allows commercial operations to be culling 6-9# birds between 8 and 12 weeks, while the meat is still tender (and largely flavorless - but tender). They don't breed true, its the better part of seven months (if you can get one to live that long) before they lay eggs, and they are not prolific layers. Cornish X Roos may struggle to get the job done. Also these birds have low predator awareness, can't escape when they do see a predator (they sort of waddle, and are flightless), and are prone to myriad health problems.
**DON'T PANIC** A few breeders have been making an effort at either putting meat back on heritage DP birds, or slowing down the CX abnormal growth to compensate a bit for its most fatal flaws. ...and if you can get a hen to age, you can get some useful genetics out of it - it just won't be a CX.
3.) Breeds True - as you are seeing, this is the kicker. The best 1) or 2) are purpose built hybrids - its just not practical for a backyard breeder to maintain three flocks to optimize production out of one, while ensuring good parent stock out of the other two. You've three choices:
A) Select a heritage breed which offers a lot of what you want - say, a white Leghorn (the classic "chicken" of most people's imagining) and selectively incubate the largest eggs from the most frequent layers, while culling the smallest, slowest developing birds for the table (and accepting that they will be small birds at the table). You can do this with a moderately small flock.
B) Select a number of breeds with desired traits, and, by selective breeding and aggressive culling, create a landrace well suited to your climate, and your specific needs. This is, in essence, what I am doing - though I had no choice in starting birds (due to the pandemic). In some ways, this has the potential to be faster towards your end goal, but you will have a LOT of unsuitables along the way - and you must maintain a larger flock size if you want to get anywhere quickly. I hatch twelve eggs every three weeks +/- potentially sixteen hatchings each year.
C) Start with mutts. I know, sounds strange - but a number of people have already cleared the road I'm travelling down, making "X" Rangers - a bird with early maturity, good to very good egg production, some ability to forage effectively, and more meat on the bones than the typucal heritage. Of course, which of those traits is most valued by which breeder is a bit of a crap shoot, but a good Ranger is inspriational. With a decent flock size, and selective culling, you can maintain, or perhaps slightly improve upon your original stock, with time. Be aware that the focus on forage ability means a lighter, more active bird - slower to table weight. Its more flavorful, but there's more chew, and the savings in feed costs is balanced somewhat against the longer time till processing.
4) Better flavor. This is
EASY! Any bird that can free range or be tractored on good greens will be more flavorful - not only because its moving those muscles (so you see more intramuscular fat, less subcutaneous fat), but because the diet itself is more varied. It also means that, compared to a store bought bird, there will be more chew - because the muscles got used. A CX will happily stand at the feed bowl and eat until its dead of fatty liver disease. Quickly. Almost no other bird will do that - certainly no breed will do that.
So, in conclusion. I don't have an answer for you. There isn't one. But don't give up - the best answer for you will depend on your circumstances and your priorities. There are a lot of possibilities to choose from.
Ask yourself (4 is easy, don't worry about that) what matters most - Do you want a "breed", or will a mutt like a Ranger suffice? (I'm being a bit unfair here, the Ranger lines are approaching a breed, rather than a mere landrace at this point). How large a flock are you willing to tolerate/support? Bigger flocks allow less frequent egg production, more meat on table, while maintain total flock size. Smaller flocks are more prone to genetic issues and higher risk of significant production loss in cases of predators, molting, etc - but they need less space, and are cheaper to feed.
Do you really want big breasts, or do you prefer dark meat? What's your climate?
Can you reasonable offer pasture for forage? How varied (again, what's the climate? and the predators?) - that will inform the free range v chicken tractor management styles. Do you have a thing for white eggs? or cream? or brown? Green (please no green!)? Incubate, or rely on broodies? How many eggs each week do you really want??? How many do you need, when production drops with daylight hours, or they go into molt... How long do you plan on keeping any individual bird??? Do you care what they look like???
Its a lot - but you are asking the right questions, and making informed choices. Not all of us found BYC before we started. Mistakes were made. Welcome!