Damn! You live in Queens and you have a porch, a yard, and a pool! I wanna live with you and get out of my 5th floor walkup 2BR with none of the above! Got any room for me?
Palms are not the easiest plants
for beginners and they tend to grow slowly.
I suggest that you start with a Chamaedorea elegans (parlor palm), Chamaedorea erumpens (bamboo palm) or a Rhapis palm (lady palm). All do well in bright indirect light.
You should know that all palms are quite particular about water and not very forgiving if not watered properly. In addition, most palms (the Rhapis is an exception) are very prone to spider mite infestations.
Avoid getting a Majesty palm at all costs.
Have I talked you out of getting a palm, yet? LOL!