Early years (during the hedge fund):
1) The "cigar butt" value-investor -- looking for companies which held more book value (assets like cash on hand, factories, etc.) than capitalization (stock price times shares outstanding). Arguably Sun Microsystems (right before Oracle bought them) and Yahoo now are pretty close to this in big tech companies, but back in early/mid 20th century, there were LOTS of these.
2) Value investing -- looking for brands which have growth potential but are undervalued by the market. Apple right after Steve Jobs returned would be a tech example.
3) Special case situations, like arbitrage -- for instance, right before a merger, buying one or the other stock, and if you have someone like Apple releasing a product which has a component from one vendor, buying that vendor's stock.
WB largely ended this strategy for two reasons: it was successful enough to use up most of the available opportunities (as well as attract copycats), and it was very labor/research intensive for the returns you could get -- good percentage returns, but it was difficult to employ large amounts of money. Sort of like angel investment vs. mezzanine IPO financing.
Mid years (70s and 80s): insurance
WB discovered the insurance industry (through GEICO), and basically had "free money" to invest (which is what an insurance company does with premiums). He went from value investing to buying entire companies (or large shares) which he thought would grow and remain good companies.
Late years: (1990s to now): top-quality
He basically has the problem of having too much money to invest, and thus can only go after the largest opportunities; a 10x return on $1m is not enough to move the needle. Thus, WB and BH buy entire top-quality companies, with a focus on sustained performance, vs. making a lot of speculative bets.
The old-school WB (and even better, Ben Graham, his early role model), is the only interesting one to me -- once he had established his track record doing something well, he was in a position to make reasonable investments no matter what. Getting to that point was the interesting part.