I've read statements/blogposts/interviews etc. from well known people in the BDSM community suggesting that breath play is simply too dangerous to do, with too many risks. I have to wonder what techniques these people are using, because I have trained for years in submission grappling, and know that all over the world judo players, bjj players, submission grapplers, and mixed martial artists are choking and strangling each other without incident. In a given class at just my school, if you add up each incident in training and drilling you probably have hundreds of strangulations a day. Given the number of people who train in these sports (judo is one of the most popular sports in the world) we're talking about a ridiculously high number of these in just one day, never mind over the years. And yet you don't hear of people dying from it.
Some factors of how we do it: well, obviously we don't use any rigid objects like a nightstick, we don't choke using things that can't be released quickly (it IS common to choke someone using the collar of their own gi, but that's hardly comparable to a belt or rope that's been tied or fastened in some way), and when possible we tend to go for blood chokes/strangulations instead of air chokes, which means we're not putting much pressure on the wind pipe most of the time. Unlike what some of the posts say above, we ARE fighting the chokes (these are competitive sports, after all), but we realize when we're caught and almost always tap out, as opposed to fighting until we've passed out. We also have high level, professional instruction in what we're doing, with supervision most of the time while training.
So my advice: stay away from using belts, bars, ropes, and chains. Start with the hand over the nose and mouth, and if you really are enjoying it, one or both of you might consider signing up for a few months at your local brazilian jiu jitsu, judo, or submission grappling school. I'm surprised more kinksters don't do this, after all, this may be the only aspect of kink where you can openly attend several classes a week with trained experts.