When choosing papaya, consider when you are going to eat it.
If you are planning to eat it right away, then it is best to choose the ones that have a reddish-orange skin and are slightly soft to the touch.
If you plan on buying your papaya a few days in advance, then choosing those with patches of yellow colour on them is the best way to go. It will take them a few days to ripen.
Black spots on the papaya do not affect the taste, but you should avoid those that are too soft or are bruised.
Papayas are usually the same way you eat a melon - raw. Make sure to give them a wash before you cut them in half. Scoop out the black seeds in the center with a spoon. then either scoop out the flesh or into pieces. If cutting them into pieces be sure to peel the skin off.
You can eat the flesh as it is or add it into a fruit salad or other recipes. Remember, you should add the papaya to the salad just before you are about to serve it because it tends to make other fruits in the salad very soft.
The black seeds are actually edible but some people find the peppery flavour quite bitter that's why most people just tend to discard the seeds. But if you are curious and maybe feeling a little adventurous, definitely give the seeds a try! They can be chewed on whole or you can blend them into dressings.