Our local farm store gets chicks every spring, and they'll sell individuals, so my first year I was able to get seven different breeds -- one of each. That way I could compare, and they were a lot more individual than a bunch of the same breed. That's usually not possible if you're ordering them, because most places have a minimum per-breed order (and the farm store here doesn't have them this late in the year). But if you can find a place selling them per-bird, you can experiment with several breeds at once.
The most productive layers are Leghorns. They're also the most efficient as far as how many eggs they produce per pound of feed. They're like little egg-laying machines. That's why they became the industry standard, and their white eggs became the most common and cheapest in the store. However, Leghorns are kind of flighty and their light weight makes them pretty good fliers, so they'd be harder to keep fenced in an urban setting than the heavier breeds. In an urban backyard, I'd go for one of the heavier brown-egg varieties. Several of those lay about the same number of eggs, so it's just personal preference: Barred Rock, Rhode Island Red (and other Red varieties), Australorp, Buff Orpington, Cinnamon Queen. The Cinnamon Queens may be a bit more productive than the others.
If you have kids, they often enjoy Ameraucanas, the ones often called Easter Egg chickens, which lay blue or green eggs. They lay fewer eggs than the others, though, so they're a novelty item.
If you plan to sell eggs, many people will pay more for brown than white, so that may be a consideration. There's no difference in nutritional quality -- the feed determines that, not the breed -- but many people insist that brown eggs are better for baking. Who knows, but it can mean another dollar a dozen.
Edited to add: None of the great egg layers are also great meat birds, compared to a true meat breed. But the heavy breeds like the Reds do have some meat on their bones, while a Leghorn carcass wouldn't be worth much more than making stock.