IMHO, Polar is kind of the standard of the industry. Any HRM you buy will be "unobtrusive." The only part visible to anyone else will be the watch/receiver, which looks like, well, a watch. You want to make sure you get one w/a chest strap as opposed to the type where you need to touch your fingers to the watch to get a reading. The reason for this is that the chest strap monitors your heart rate 100% of the time, sending the info wirelessly to the watch. The other type only gets a reading when you touch your fingers to the watch. This would clearly affect the accuracy of the reading. The chest strap is about an inch and a half wide w/a plastic piece in front housing the electronics. No wires, no antennas, no reason for anyone to see this--if you're female, it sits right under the lower edge of your bra and you really don't notice it after a minute or two. Can't speak for the male point of view but imagine that you also tend to forget about it as you start exercising.
If you go to the Polar website, you can compare all the features--you can get these so simple that all they do is monitor your heart rate or so complex that they will monitor 5000 laps of 10 different sports at one time and will also wash your car and pack your lunch. Prices vary accordingly, but decent ones are available for well under $100 that will give you heart rate and calories burned. They are also pretty much indestructible (at least in my experience) so it's a long-term investment, not something you will need to replace yearly.
Think that's about all I have to offer--hope it's helpful.