If you're looking to invest in the restaurant business but have no desire to be involved in the messy day-to-day operations, you're in luck. Through the stock market, you can literally pick from dozens of promising publicly traded restaurants. By purchasing shares, you can literally own -- and profit from -- a small slice of the underlying business.

But not all restaurants are created equal. The best investment candidates are solidly profitable and efficiently run, have enduring brands, and ideally have potential for sustained long-term growth. Moreover, some restaurants dominate or show great promise within their own niche, whether it's fast food, casual dining, or the more recent hybrid of those models in fast-casual dining.

I've chosen three of my favorite restaurant stocks, including one from each segment.

Fast food: tacos, pizza, and chicken

Among the many fast-food restaurant concepts, I think Yum! Brands (NYSE:YUM) is currently the most intriguing. As the parent company of Taco Bell, Pizza Hut, and Kentucky Fried Chicken, Yum! Brands operates more than 40,000 restaurant locations worldwide.

But though it's a nearly $32 billion company today, Yum!'s growth isn't done yet.

In fact, last year Yum! outlined plans to double U.S. Taco Bell sales from $7 billion in 2012, to $14 billion by 2021 -- a lofty goal considering total company revenue in fiscal 2013 barely exceeded $13 billion. But it seems more reasonable as Yum! notes that the growth will come from a combination of new dayparts -- including this year's nationwide roll-out of Taco Bell breakfast -- and increasing the number of U.S. Taco Bell restaurants by nearly 40% to a total of 8,000. For perspective, Yum! competitor McDonald's operates more than 14,000 locations in the U.S. alone.

A KFC restaurant in China. Credit: Yum! Brands.

Or take China, where Yum! generated 44% of its total operating profit in 2012. However, KFC and Pizza Hut are currently struggling in China given the fallout from quality issues with a supplier -- and that's only the latest in a string of similar bad publicity in the country for Yum! But management insists that business in the Middle Kingdom will return to normal over time. As of the end of last quarter, that's why Yum! was still on track to add as many as 700 more locations in China by the end of 2014.

With shares down 4% year to date and trading at a reasonable 18 times next year's expected earnings, and given Yum! Brands 2.1% dividend, I think the stock could be poised to handsomely reward patient investors from here.

Fast casual: burritos (with integrity)

Fast-casual restaurants aim to strike an attractive balance between the value and convenience of fast food, and the typically higher-quality wares of more expensive casual-dining brands. Arguably no chain has harnessed that balance as well as healthy-burrito maker Chipotle Mexican Grill (NYSE:CMG).

Credit: Chipotle Mexican Grill.

By strictly following its "Food With Integrity" mantra -- under which it strives to find "the very best ingredients raised with respect for the animals, the environment, and the farmers" -- Chipotle has profitably grown to more than 1,600 locations since it was founded in 1993. Better yet, Chipotle's success only appears to be gaining steam: Revenue in its most recent quarter grew 28.6% year over year to $1.05 billion, driven both by new restaurant locations and a 17.3% increase in comparable restaurant sales -- the latter of which was its best result since early 2006.

What's more, Chipotle expects to end 2014 with 180 to 195 more locations than what it started with, all as comps continue to climb in the mid-teen range. Chipotle is also hedging its bets with two more early fast-casual concepts, including seven ShopHouse Southeast Asian Kitchen locations, and an investment in an entity that owns and operates one Pizzeria Locale restaurant.

But Chipotle stock certainly doesn't look "cheap," trading at around 62 times trailing 12-month earnings, and 38 times next year's estimates. But given Chipotle's solid profitability, amazing customer loyalty, and impressive growth prospects, I think that's a small price to pay for this superior restaurant business.

Casual dining: beer, wings, sports

Finally, growth in the casual-restaurant industry has remained sluggish the past several years, but don't tell that to Buffalo Wild Wings (NASDAQ:BWLD).

Credit: Buffalo Wild Wings

To be sure, B-Dub's fanatical focus on creating an engaging dining experience around beer, wings, and sports helped it grow revenue and earnings by 20% and 42%, respectively in its most recent quarter. For all of 2014, Buffalo Wild Wings expects earnings to increase as much as 30% year over year, thanks both to the opening of 85 new restaurants and solid same-store-sales growth in the mid-single-digit range.

Of course, that's not nearly as impressive as Chipotle's mid-teens growth in comps, but consider this: Buffalo Wild Wings also has a minority stake in a small, Chipotle-esque Pizza chain called PizzaRev. And only a few weeks ago, it announced a majority investment in a nine-restaurant street taco specialist called Rusty Taco. Long story short, Buffalo Wild Wings is following through on an earlier promise to investors that it will eventually become a 3,000-restaurant chain built on a portfolio of diversified, complementary brands. 

As a long-term Buffalo Wild Wings investor myself, I'll definitely drink to that.

Steve Symington owns shares of Buffalo Wild Wings. The Motley Fool recommends BMW, Buffalo Wild Wings, Chipotle Mexican Grill, McDonald's, and Nike and owns shares of Buffalo Wild Wings, Chipotle Mexican Grill, and Nike. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.