A nice, slow-acting poison allows the recepient to croak several hours after administration, often in their own home. If you're smart it will biodegrade quickly and leave little or no trace for some smart-aleck forensic toxicologist to find. Most importantly, someone else has to deal with the mess of disposing of the body, cleaning up, and so on.

Throttling is okay too, as long as you tie off your victims pant legs at the ankle. Done correctly the hyoid bone might not even be broken.