After a mild Heart Attack and cardio rehab, I use a Polar F6 which is fine on bike, running and the pool (and counts cals).
I think any of the big makes are good, Polar, Sigma et al, it's just a case of choosing what functions you want.
I find, the alarm important if you are BPM limited and also the "coded" function which prevents picking-up signals from other HRM's. Other than that, just go with what looks good and displays what info you want!
Files and Data transfer stuff is all beyond me!
Whilst not suitable for swimming, but suitable for cycling and running. I have a kalenji cw300 coded from decthlon for 30 quid. I've used it a lot, even with sweat pouring off me and it hasn't skipped a beat (excuse the pun). Great value and seems to do stuff similar to a far more expensive polar hrm at a fraction of the price. That said, I havnt had a heart attack so you may feel better forking out more money for a well known brand. (for reference the readings on this seem to be spot on, compared it with a pulse oximeter heart rate reading, hrms on the gym equipment and also the old fashioned method and it's agreed with them all)