I am non-op. Not pre-op. There is a difference.
First and foremost, I must address the fact that my experiences, beliefs and lifestyle do not conform to that of the majority when it comes to trans* people. I am more comfortable with the body I was born with than even some non-trans people. I don't see anything wrong with it, and while I would like to have a perfectly flat chest, I will not go through surgery to get it. Had I been born with a chest larger than the one I have, I would want top surgery.
A wise FTM once said, "the beard trumps the boobs" and he was right. Once I started consistently passing, I pretty much gave up on actually binding. I still wear a tri top binder from underworks, but I wouldn't consider it binding. I wear an XL tri top and it fits me like a snug athletic shirt. It's just enough to hold me in. I no longer see the point in binding tightly and making myself uncomfortable when I look fine with the bare minimum.
I've used different types of binders over the years, and underworks is by far my favorite. Although all binders do have their use.
Ace bandages, however, DO NOT always work for a binder. If used too tightly, they work like a boa constrictor. I have never tried them, but plenty of people have. They are designed to tighten anytime they get the chance. When you breathe in, they expand, and when you breathe out, they tighten even more than before. You can do serious damage to your body by using them. I don't suggest using these bandages at all. Or tape of any kind. There is one exception to ace bandages, however, and that is that some surgeons will have you bind with ace bandages after surgery. Similarly, some people can bind with ace bandages and not do damage to their bodies. This is because they know how tightly to wrap it. I've never tried it, and I don't recommend it, but if you are going to try it I would recommend doing it at home where you can unwrap yourself quickly if you wrapped the bandage too tightly. The bandages themselves are not the problem -- it's how tightly you wrap them around your body and other individual factors. Basically, some people can do it but most people can't. I still don't recommend them.
The back braces made of neoprene and similar things are good for binding flat. They are adjustable and are basically one size fits all. They tend to slip though, and they make your stomach stick out more. They can also make your chest look like a "speedbump" if you don't pull your chest out to the sides. The compression is there, though... if you're willing to forfeit breathing. The cost is less than $20. (The Franklin A1 from Target is what I used)
The zippered vests of any kind work wonders. These give you maximum compression, literally. The pressure disperses in all directions and the material is thin enough to allow your chest to flatten evenly. You really need some sort of pull from over your shoulders to achieve full compression. This is why these vests are great. They are expensive, though, at around $80. (Morris Designs, Mango Products).
Underworks has so many binders on ftm.underworks.com that it's hard to know what will work best for you unless you have tried them. The tri top and the double front are the most popular binders from Underworks. They are made of a stretchy material -- lycra and spandex -- and come in a variety of cuts and strengths. They range from one layer of binding power to three layers.
I have had binders made from this material with one, two and three layers. Binders like these made from one layer are and not very workable unless you are practically a stick and have no body fat or chest. The general rule is the thicker the binder is, the less likely it is to roll. But if it's extremely tight it might roll no matter what. It also depends on what clothes you are wearing. If your shirts come untucked easily because of activity, then your binder may roll no matter how thick or long it is.
The two layers in the Double Front (Style 997) don't work for me and it is too long (goes past my hips) but the three layers in the Tri Top do (Style 983). The Tri Top is also the best length for me. It only goes a couple of inches above my belly button. I only use the Tri Top. I don't want to have to deal with tucking something long into my pants and worry about it rolling up on me. Plus, it is uncomfortable to wear that long of a garment. I sometimes fold up the excess from the bottom of the Tri Top if it starts rolling.
Underworks says to wash their products in only cold water and never to put their binders in the dryer, but I always wash mine in hot water and dry it with the highest heat possible every single time I wash it. If your binder loses elasticity, this is good. Otherwise, don't do what I do if you already have a hard time putting your binder on. My case is different since I need it to shrink slightly after I wear it out. I wear mine larger than most people. It shrinks about 2 inches when I wash and dry it this way.
I've used the frog bra but that doesn't work for me. Plus it's a bra. Enough said.