Hey Bacon, getting a binder was a big thing for me, so hopefully I'm able to help you out. Love Boat, I've never tried, but I've heard mixed reviews, that they don't last long, but they bind well for some people. Underworks is probably the most popular, and most people buy the Tri Top product, and get good results, but it is uncomfortable. I use GC2B binders, and I love them. They are comfortable, not stiff, and bind well (I'm on the medium side).
I have no idea what my cup size is either, but if you go on each website, they should have instructions for measuring yourself to see what size you would fall into (Small, Med, LG, etc.). Your height doesn't matter so much, because there are half top binders, and full length ones, so you can choose what you'd like. And if you're a bit curvy, you may want to try some compression shorts or a full length binder.
I believe that ordering one is pretty discreet, I know the GC2B was, it's hard to tell what it is until you open it. If you want something that will probably bind the most and can be a bit uncomfortable, you would probably want Underworks. I dont have much info on Love Boat, but it may be worth a shot, idk. GC2B though I think wins on comfort combined with binding ability imo.