For instance, could a person build a suit that went against gravity enough that you could go through a black hole and survive?
To the best of our knowledge, no. There are 2 BIG problems to consider. The first is how to nullify gravity. We have no way to do this at present. You can act against it - you can jump, for example - but that does not eliminate the gravity acting on you, it just counteracts it. You can act against any force of gravity, but that won't stop it from tearing you apart.
The second is the nature of black holes. We still know next to nothing about them. You mention going "through" them, but we don't even know if there's something on the other side to go "through" to. Ideas about what happen to you past the event horizon are just speculation.
Hand-wavium is pretty much all that can get you where you're trying to go. You can research theoretical physics to make your explanation sound more plausible, but ultimately, you're going to be making stuff up.