I do feel it works better to use RCs as a means of proving one is dreaming, but not to prove that one is not dreaming. I say this because RCs sometimes like to troll me and indicate reality during a dream (and depending on my lucidity at the time, I may or may not be fooled by this), but it's pretty much impossible for a well-chosen one to indicate dreaming when awake. So, I don't tell myself that I'm not dreaming when I do a RC in waking life, but rather that I simply haven't found evidence that I'm dreaming yet, and I try to encourage myself to continue keeping my eyes open for such evidence rather than simply forgetting about it and going back to what I was doing.

As for some types of RCs working better than others, I can't speak for that. I wouldn't be surprised if it varies by individuals, perhaps based on their schemata/expectations. I mostly use digital watch/text-checking and/or flying/hovering since they're the first ones I used and I found them sufficiently reliable for me.

It's probably not unusual, either, to do an RC after becoming lucid rather than the other way around. This is usually what happens to me: I suspect I'm dreaming first, and just use the RC to prove it to myself so I can be confident I'm dreaming and then go about my usual LD stuff. Even so, though, the RCs still seem to help with having LDs, perhaps because they encourage the user to develop a sense of self-awareness and critical thinking about their state of reality when done regularly.