Last year 2014 I planted a bunch of mexican Papaya seeds and subsequently ended up with a bunch of Papaya seedlings. These guys are relatively easy to grow. It just takes about 1-2 months to germinate. So be patient. Mexican papayas tend to be larger plants but mine have been in pots all their life and they have stalled a bit.
They seem to do better in morning and afternoon sun then partial shade in the afternoon heat here in Seattle.
I overwintered just 2 plants indoors and they are still thriving and doing well. Who says you can't grow tropicals in Seattle?
Here they are at 2 yrs old. They are about 3ft tall