I have these questions all the time and this is the process I go through in my head. Examine what you need the line to do for you and you will find the answer. First, since you want to "try some deeper cranking" it's probably important that you have a "sinking" or "neutrally buoyant" line. Any line that floats will curb your depth. This would suggest fluoro, a co-poly such as Yo-Zuri Hybrid, or a braid like Sufix 832. Mono eventually sinks because it becomes waterlogged. That's not the same as being a sinking or neutrally buoyant line. As a result mono COULD cause your deep crank to run not so deep. I say COULD because there may be some other factors I'm not aware of and because I don't want to be viciously disemboweled by the more experienced guys on here that are die-hard mono guys.
Second, you mentioned you might be dragging them through some roughage. Abrasion resistance and strength are paramount. Braid tops that list followed by flouro, hybrid, and finally mono.
Third, you will want some east-of-casting/distance. I can only list my own experiences with this as a guy with just one year using baitcasters under my belt. Mono wins this one for me followed closely by Yo-Zuri Hybrid. I have no experience with fluoro so I'm of little use on that topic.
Fourth, you may be concerned with "feel". Perhaps you aren't, but that's a huge thing for me. Especially with things I'm not used to fishing and while I've got years of experience with topwaters and jerkbaits, I have little experience with deep cranks. I need to be able to feel that crank moving and the bump of the bite. Especially when I'm knocking the crank off of logs/rocks/bottom. For me that puts braid at the top followed by Yo-Zuri Hybrid. Mono (for me personally/not an expert) is so bad that it's a no-go. I can't feel a darn thing with mono of any kind that I have tried. Not compared to braid and hybrid. Again, no experience with fluoro.
If you are so inclined, pick what is important to you from these questions, weigh how important each is, and then pick the line that fits best what you are most concerned with. My deep cranks and lipless cranks run on Yo-Zuri hybrid (and occasionally on Sufix 832). And I'm having success catching good fish with them which encourages me to practice with them more often.
This is advice from someone who is learning right along with you. Don't ignore the experts and experienced guys on here. They have improved my fishing tenfold.