Has the bear market finally given way to a new bull market? Maybe. Although stocks have only been choppy of late, we've seen a few flashes of bullish brilliance since October. It's certainly arguable that we're nearer the end of the bear market than not.

With that as the backdrop, here's a closer look at three stocks you might want to own at a new bull market's onset: United Rentals (URI 2.63%), Nvidia (NVDA 0.17%), and Ulta Beauty (ULTA -0.35%). These tickers were among the last bull market's biggest winners. And their respective company's products and services are always in demand during economic growth phases.

These stocks dished out quadruple-digit gains between 2009's low and 2021's high. While it may be tough to muster the same-sized gains again during the next bull market, there's little doubt all three companies have the right stuff to thrive once the global economy is booming again.

United Rentals

Let's look first at United Rentals. There was a time many years ago when companies debated purchasing equipment versus renting it when needed. The cost of buying equipment has outpaced inflation since then.

Yet, so has the availability of rentals. Both trends favor tool rental outfits like United Rentals, which offers short-term access to everything ranging from tile saws to scissor lifts to backhoes, and more. Assuming a new bull market coincides with economic growth and stabilizing interest rates that in turn spark a new housing boom, this company could sizzle in the years ahead.

Still, it wouldn't be a completely crazy idea to let United Rentals shares fall back from their recent record high just a bit if you're interested. It looks like most investors are seeing the same dynamic, pre-emptively buying the stock for what looks like a very bright future.

Nvidia

Technology is also always in demand, but some types of technology see especially high demand when times are good and corporate profits are strong. Nvidia makes a great deal of this tech. In fact, its graphic cards account for more than 80% of the world's graphic processor sales, according to John Peddie Research. Video gamers love them, and an ever-growing number of computer animation and design professionals do as well.

Nvidia's big breadwinner during the next bull market, however, won't be graphics processing units meant to generate a visual display for users. The company's next big growth engine is artificial intelligence. As it turns out, the same tech that makes great graphics cards also makes for great machine-learning equipment. That's why Nvidia's hardware is already found in the majority of the world's most powerful supercomputers, including the most powerful one owned and operated by Facebook parent Meta Platforms.

In light of this reach, Precedence Research's expectation that the AI hardware market is set for annualized growth of nearly 30% through 2030 bodes very well for Nvidia. A bull market will only bolster the stock's potential upside.

Ulta Beauty

Finally, add Ulta Beauty to your list of the next bull market's potential mega-winners. It rallied more than 7,000% from its early 2009 low to 2021's high, and then somehow defied last year's bear market to now sit nearly 10,000% above the bottom made just 14 years ago.

Another gain like that is unlikely. But another market-beating advance is hardly out of the question. That's because the chain of more than 1,300 cosmetics, fragrance, and skincare stores is striking the perfect chord with consumers, offering a combination of affordability, accessibility, and connectivity. Although the company offers online shopping, the stores themselves are where most of the personal relationships with customers seem to be established and then maintained, with an assortment of more than 25,000 different products.

Other retailers may look similar. Ulta is differentiated, however, in the ways that matter most. Its value proposition means it can stand up to weak economies. When times are good, though, it can truly shine by catering to consumers' splurges.

Just keep things in perspective

Again, just because these three stocks performed outrageously well during the previous bull market doesn't mean they'll repeat the feat in the next one; they probably won't. Most major winners are unexpected, often "coming out of nowhere," so to speak. The next bull market isn't apt to be different.

Also know that while it's not too soon to start reorganizing your portfolio for prolonged bullishness, there's no guarantee last year's bear market is over. It's possible we could see new lows before all is said and done.

On the other hand, the biggest risk that investors face isn't suffering a little bit more downside, but instead missing out on the full potential of a new bull market from its onset. A huge piece of a long-term bull run's gain takes shape at the very beginning of a bull market.

Either way, all three of these stocks are meant to be long-term positions based on their previous results and their underlying company's future growth prospects. It doesn't -- or shouldn't, anyway -- entirely matter if you step in at the exact bear market low. The only exception to this line of thinking might be United Rentals, only because it  has ignored marketwide bearishness and has soared since October.