As the others have said, the first two sentences are about the same in meaning. "you should" is more formal ("you'd better" is a colloquialism), so in any formal setting (essay, email, business), I'd recommend using you should. "You'd better" can also be used in a threatening way, e.g. "You'd better not come back here, or I'll break your neck." In American English, rather = prefer. So the difference between these two sentences is: I would (be willing to) use this way, but I would rather (prefer to) use a different way. In British English, it is common to use "rather" to offer an alternative. E.g. "You could take this route, or rather, you could take this shortcut." (Rather can also mean somewhat: "I'm rather tired." But in general, neither of the sentences you've listed sound very natural in English. If by "way" you mean "method," you should say, "I'd do it this way." / "I'd rather do it this way." If by "way" you mean "route/road," you should say, "I'd take this route."/ "I'd rather take this route." :)