An alternative to Natural Selection would be something along the lines of inheritance of acquired characteristics, otherwise known as Lamarckism. Inheritance of acquired characteristics was disproved early on, but it was one of the first mechanisms for evolutionary change that was hypothesized. Sexual selection is not really an alternative to natural selection in the meaning of replacing it, but it is an alternative mechanism that can drive evolutionary change. Sexual selection is different than natural selection, because the most fit individual for the environment is not the one that will necessarily leave the most offspring. In the example of the birds of paradise, a male with a shorter tail would be better suited for the environment, in the sense that it could avoid predation longer leading to a longer life, which means it has more chances to have offspring. Instead the female selects a male with a long tail, which makes him less fit for the environment, but he will leave behind more offspring than the short-tailed more fit male. The argument from the good gene hypothesis of sexual selection has only been shown to be true in one paper, so it can't be assumed to be the norm. You might be more entertained by looking at the ideas of different levels of selection. This includes the good gene theory, the unpopular and not strongly supported hypothesis of group selection, and individual selection. It would also be useful for you to understand ideas like kin selection, which is explained by the good gene theory, altruism, and maybe also take a look at evolutionary game theory.