Mechanical keyboards are better than membrane keyboards in every way, but it's a matter of picking which mechanical switches to get depending on your needs or preferences.
Blue: tactile, audible click. Great for typing. Probably not ideal for osu! (and arguably other games) since the depression point is lower than the release point, making it somewhat more difficult to rapidly press.
Brown: slightly less tactile, non-audible click. Much lighter to press compared to Blues. I have one of these, and other than the click, they feel like reds. These work for general purpose, as they're good for gaming and good for typing. The click is at the same point both ways. In osu!, the lightness helps for streaming, and the click helps for accuracy.
Red: No tactile click. These are the lightest type of keys, and because of this they're great for streaming. Some people like these due to how easy and fast they are to press down, but for typing they aren't ideal as it may lead to spelling mistakes.
Black: No tactile click. Stiffer than the other keys. I haven't tried these, but they're generally good for gaming since you don't really need a tactile click if you're going to be holding them down most of the time (for games such as FPSes). The stiffer switches help prevent accidental presses, but they might also make it more tiring to stream in osu!.
With the information above, keep in mind that preference is a factor in picking a keyboard. Personally though, I'd say that if you're getting a keyboard just for osu!, get brown or red switches, depending on if you want your keys to have a tactile click or not.