I would also think that stocks would be the first ones to stabalize or even increase because companies have the ability to increase prices in a high rate environment.
You might think so, but prices tend to be sticky. Some types of products (i.e. name brand consumer goods) find it very difficult to raise prices, because consumers will substitute other cheaper products. Sometimes utility companies are regulated by the government and are prevented from raising prices.
Technology/Internet companies that don't have a lot of expenses tied to commodities or shipping/distribution costs MAY
be in a situation where their profit margins aren't so tightly squeezed, but they're also one of the areas it's easier for consumers to cut back on.
Energy/oil will be needed to keep things moving if the economy really gets going.
But none of this is new information, the stock market tends to anticipate all this, and if we think it's missing something - it probably means it's anticipating other factors we're not considering. Any trade you make will have someone on the other end of the deal who believes something else.