A new bull market is here -- or almost here, depending on your perspective. Some investors declare a new bull market for the S&P 500 when the index rebounds at least 20% after falling by that amount or more. Others demand that the S&P also reach a new high.

However you look at it, Warren Buffett has several excellent candidates to consider in Berkshire Hathaway's (BRK.A -0.76%) (BRK.B -0.69%) portfolio. Here are my picks for the three best Buffett stocks to buy and hold in a new bull market.

1. Apple

Buffett absolutely loves Apple (AAPL -0.35%). And his treasure lies where his heart is. The tech giant ranks, by far, as the biggest holding for Berkshire.

However, I didn't put Apple at the top of the list to buy and hold in a new bull market just because Buffett thinks so highly of it. I have two other primary considerations.

First, it will be next to impossible for a new S&P 500 bull market to have legs without Apple stock performing well. Apple makes up around 7.5% of the index.

Second, Apple truly is what Buffett would call "a wonderful business." The company doesn't just have customers; it has fans. Apple's iPhone stands at the center of an immense ecosystem of products and services.

Don't let Apple's fiscal 2023 third-quarter revenue decline fool you. The company continues to have solid long-term prospects.

2. Amazon

No, Buffett didn't personally make the decision for Berkshire to first invest in Amazon (AMZN 3.43%). Nonetheless, he admires the company.

It might seem strange to call Amazon a turnaround story with its stock skyrocketing this year. I think the description is appropriate, though. Amazon really is turning its business around after enduring a semi-slump.

That's especially evident in the company's bottom line. Amazon lost $2 billion in the second quarter of 2022. Last week, it reported a profit of $6.7 billion in the second quarter of 2023.

The story is similar when it comes to cash flow. Amazon generated free cash flow of $7.9 billion over the trailing 12 months ending June 30, 2023, compared to a cash outflow of $23.5 billion in the trailing-12-month period a year earlier.

I think artificial intelligence (AI) will provide a major long-term tailwind for Amazon's cloud business. And I expect its streamlining in recent months will continue to pay off with improving profitability.

3. Markel Group

Markel Group (MKL -1.00%) can accurately be called a "mini-me" of Berkshire Hathaway itself. It has a large insurance business, owns a diverse portfolio of stocks, and invests in other businesses.

Just like Berkshire -- almost. There are a couple of key differences between Markel and Berkshire that I think make it a great Buffett stock to buy and hold in a new bull market.

Importantly, Markel is much smaller than Berkshire. Its market cap of below $20 billion is practically tiny compared to Berkshire's market cap of close to $780 billion. In my view, Markel's path to growth is easier because of its size.

Markel also invests in growth stocks more aggressively than Berkshire does. It owns shares of companies like Alphabet and Meta Platforms (as well as both Apple and Amazon), all of which should perform well in a new bull market. I also expect Markel's core specialty insurance business will chug along nicely.