Tracking backwards a bit, I answer you with story time:

While my hair isn't curly, it is super wavy and flippy.  I got my hair cut for the first time in 13 years last year in October, so I went from really fucking long to a short flippy asymmetrical bob-ish thing.  I had, a few months before that, given myself an undercut by just shaving the underside of my head bald.  Shaving that stuff off was actually one of the most freeing experiences of my life, and, in the wake of a lot of trauma, felt like the first time I was in control of my own body.  It’s amazing.  

So I was a little frustrated that my stylist would not listen to me when I went to get a proper cut.  I told her that even when it was three feet long my hair was wavy, and she’d need to accommodate that.  She proceeded to ignore me and straighten my hair in order to cut, which I really was angry about.  I hate how my hair looks, feels, and behaves when straightened, not to mention I’m not wild about the damage it does.  I told her I’d never be doing that to my hair and wanted a cut that would behave well with my hair natural, but she was pretty determined to cut my hair the way SHE would wear it.   Later, when my hair recovered and began to grow back, you could tell that was a big mistake on her part because it stuck out really wildly.  I liked the flippy bits to some degree, but only after it had filled in a little.  There was an awkward time in the first week or two that it just did weird shit.   She learned from her mistake and never took a straightener to my hair again, but I only went to her two more times after that.  

Now I have to find someone else and try to make them understand that I want my hair very obviously asymmetrical, and I want most of it buzzed down in an undercut-ish fashion. The last girl I went to kept saying that getting it too short wouldn’t be feminine and I just gave up protesting because I felt like I was taking up too much time there, though I should have fought more because it still wasn’t as short as I wanted.  

So as far as what I’m getting, I don’t really know yet.  I want something a bit ‘edgy’ or scary, really.  I love asymmetry, and I loved the way my hair feels shaved down to peach fuzzy stuff, and I love my wave, so I want all those things incorporated. I want some twisty and soft and I want some strange and sharp, because I think that combo is my whole personality. I have a lot of looks saved that I like, but none I’m totally settled on.  I’m hoping the stylist I was randomly assigned this time will be willing to work with me and make something good from the images I bring and my general day to day needs.

SO, WITH THAT BACKGROUND OUT OF THE WAY, ON AN ADVICE FRONT: 

I feel like you would not be out of line to call ahead to some place and just say, “Hey, I have super curly hair, do you have someone who specializes in this?”   And then, frankly, if not, just go find somewhere else, because it’s worth it.  I noticed a difference when a person who specialized in short funky hair did my cut versus a person who normally does very pretty generic cuts did it.   I also definitely noticed a difference in how things went when the person doing the cutting let my hair do its thing and worked with it instead of treating the whole process like a rodeo and roping stragglers.

 When you find someone, show up with photos or references or something.  Even if the stylist can’t make that exact thing on your head for whatever reason, if they know what you LIKE, then you can both sort of work together and get something that flatters you and fits your aesthetic.   (Or you can aim for that.  If you’re in a spot where you’re playing stylist roulette like I am, you just sort of hope this person is on their game.)

Because the cuts I want are weird, and my hair is suuuuuuuper thick and has a bunch of wave, I haven’t yet braved a Supercuts or something, and have only gone to little salons and things.  It might be worth it for you for the peace of mind (and not having to pay someone to un-fuck it up) to go somewhere that might be a little more expensive.

I speak as someone who has had like five haircuts my whole adult life, so I am not a super great font of wisdom on this topic (unless the topic is specifically going from sitting on your hair and shutting it in car doors one day and kind of a sassy asymmetrical flip the next), but it’s your head, and your money, so you should be able to direct what happens to both of those things., or at least make a good bash at it.

If you’re worried that the undercut stuff won’t look good with curly hair, I would say do not worry!  Look how goddamn gorgeous these people are!