Hard science fiction has no way of believably having FTL travel, since we can quite easily observe causality and relativity, and that's incompatible with FTL.
While wormholes are theoretically possible (providing one figures out how to generate negative energy) they require an impossible amount of energy (impossible, not impractical). Even given some kind of future advancement of science and technology that found some other way of achieving FTL, that would consequently mean relativity or causality go out the window. Most likely causality (it's much less proven than relativity), a result that makes things ... complicated.
You an however still write perfectly hardish SF by just glossing over that an using some kind of magical FTL drive. I'd personally recommend using any kind of discontinuous drive, it's more believable that way to simply ignore the causality problems. For believability, what kind of description you write and what rules you set for the drive doesn't matter half as much as staying consistent with the rules from then on, and seriously thinking through the implications of a drive like that being available.
If you're writing space opera, don't sweat the small stuff. Make it generally consistent, and avoid midichlorians, and it'll be perfectly fine. David Weber is an extremely successful example of using technobabble to gloss over the lacking realism of his FTL drive. (and the STL drive!) Heck, he writes military space opera and the weapon technology and battles he describes are totally ridiculous given the FTL and STL technology those ships supposedly have. And people don't care too much. Though he likely doesn't sell to the same kind of readers that read hard SF of course. The genre you aim for defines the minimum of realism and consistency. Though of course, more realism and consistency never hurt, if you write an exiting space opera with big drama and big battles AND a high degree of realism you have an even bigger target audience.
Addedum: Please don't use black holes though. It's just a name, they're not holes, and travelling through them is very fantasy-ish. Using a small one to power a drive or generate gravity or some other purpose is fin(-ish) but no reappearing on the "other side of a black hole" please. That's almost worse than that episode of ST:Voyager where they describe the event horizon as an energy field ... and proceed to blast a hole in it.