Which one should I choose?
There are three factors to consider: the base station, the range, and the size of the headphones.
Taking the last of these first, IR and radio tend to be larger, over-ear headphones, as they need to enclose larger batteries, while bluetooth headphones are available in a wider variety of designs from traditional over-ear to funky lightweight headsets incorporating microphones (for use with your mobile phone).
The base station for IR and radio will need a power socket. Wireless refers to the absence of a wire tethering the headphones to the source, not the entire contraption. Mine (Sony MDR-RF800R) have three wires coming out of the base station: power supply, audio connection (plugs into the headphone socket), and a wire to plug into the headphones themselves to charge them. The presence of these wires makes it a chore to move them from the TV to the hifi or computer and in practice I don’t do it.
The range may seem like a limiting factor, but it really depends how you want to use the headphones. IR headphones seem to me to be ideally suited for TV use - you need to be able to see the TV, so if the base station is on top of the TV, the headphones will be able to see it. Also, you tend not to walk around the house watching TV but will more likely sit directly in front of it at a distance of about 2 or 3 meters.
Bluetooth, on the other hand, has a similar range, but you are probably carrying the source (MP3 player or mobile phone) about your person. You are unlikely, in this situation, to have a power socket following you around, so Bluetooth, if you must have wireless, is the only answer.
The greater range of radio headphones makes them well-suited to general listening where you might be in one place for a while, then want to move somewhere else. I use them at my computer, sitting on the sofa and cooking dinner.