The New World is ripe for opportunity - and failure. You can easily gain large incomes from this region with little or no effort, but you can also gain small income from here with intense effort.

How do I fail? How can I prevent failure?
You fail by picking the wrong region to conquest, usually running short on food & having low public order. Farms or Ports (either military or trade ports, it does not matter) are excellent ways to stop your people from starving. Even a 'Meagre Yield' Farm or a 'Very Poor' Port are still good for use, due to the major fact that the Americas is heavily disadvanced in the terms of technology and population.
What you might look like:

There are three Religions in the New World - Protestantism, Catholicism, and Animalism.
Protestantism:
This religion is definantly the most common religion in the New World. The United Provinces, Great Britian, and the Thirteen Colonies are all Protestant. Pirates are also considered under the Protestant religion.
Catholicism:
Second most common religion in the New World. France and Spain are the only two Catholic religions in the region.
Animalism: This religion is the third and final religion in the New World. It belongs to all Native American nations.

Side Note: Keep in mind that culture in the new world does not matter; if your villages develope faster as Animalism than Protestant/Catholicism, then go with Animalism, until you are positive you can handle yourself. But if you're having trouble keeping order with the Animalism religion, I suggest you go your normal religion.

Your worst enemy in the Americas are Pirates.
You should destroy the faction ASAP! Otherwise you're going to have one heck of a time maintaining trade. However, you don't have to destroy them, but their two little cities in the Carribean/South America area are ripe for conquest - and have great trade opportunities. The northern city they own is called: Antigua, Leeward Islands (which is a string of islands shared with france), and San Jose De Orua, Trinklad & Tobago. (Sorry for bad spelling).
Both of these settlements contain the most basic of military ports, Shipyards. Antigua starts off with Military Governor's Encampment and no settlement defences. It also starts off with Dirt Roads. It's port is in the starting condition of 'Poor' and it's Sugar Plantation has a High Yield.
San Jose starts off with a Governor's Mansion, a 'Low Yield' Sugar Plantation, no settlement defences, and a 'Very Poor' port.
Pirate cities have a bunch of Pirate Mobs in defence.
However, if you're at war with France, a good place to take along that same string of Islands would be Martinque, Windward Islands. It starts off with a Governer's Residence, no settlement defences, an 'Abundant Yield' Sugar Plantation, and a 'Growing' port. This port is also a Trading port.

Screenshots just show what they look like, not what buildings and defences they have.

Native Americans are entirely neutral to you unless you make Republican Reforms. If you're a Republic, they will hate you, but won't go to war.
Two ripe-for-the-pickings natives are:
Pueblo Nations. Despite it's plural name, it's only one small settlement, Villa de Bexar, Texas. This settlement has 1 Village, 1 Farm (Corn, Meagre Yield), 1 Harbour Village, and 1 Plantation (Cotton, Meagre Yield). It starts out with no settlement defences, and a Gunsmith. It also has Dirt Roads.
Don't want to get up close and personal with Spain, France & Great Britian? You don't need to. More north, in the Canada/US border region the Plains Nations have a small settlement, Yankton, Black Hills. You can either approach from the south, through Wilderness (Llano Estacado), then through the Wilderness (Great Plains). Or, you can approach from the north, in Wilderness (Manitoba). Yankton contains a Farm of 'Average Yield' (Corn), a Village, Furs of 'Abundant Yield'. Yankton has a Gunsmith, and Dirt Roads.
One nation to avoid is the Inuit Nations.
You'll have low public order all over the place, and people will be starving everywhere. It's not worth the resources, for such low income. They also like to rebel, despite a large garrison. Oh, and remember if France is at war with you they CAN march from their little Newfoundland island and get all up and personal with you.

Pueblo Nations (Below)
Plains Nations ^^^^^^^^^

There are, of course, Europeans in the Americas. You've got Spain, in mexico, Britian, who owns a few territories near the Carribean, and one in Canada. The Thirteen Colonies (Britian, pretty much), France, who owns territories spread throughout the area: US, Carribean, and South America. Finnaly, the United Provinces own a small settlement in South America.
I do not suggest going to war with a nation JUST for territory over the Americas, due to the fact that (Europe, for Europeans, India for Indians, America for Americans..... you get the point.) To help prevent this, get those isolated areas (Iceland in Europe, Ceylon in India). Although, if you are at war with somebody, the New World is a great place to stop and shed your enemy's blood and take a few places when you'd like, since the Americas aren't very advanced.

It is a good idea to use your allies when you want to move into the new world. How so? At one point, you're probably going to go to war with somebody who has territory in the new world. So hey, let's have our allies distract the enemy in europe so we can sneak around to get more land! Excellent idea is excellent. They still will have military force, but I usually find that they are weaker than before, or at least have less units.
Occasionally this plan won't work right. They'll still keep some powerful stuff behind, if they had it there in the first place.

Growth Stimulation from the war with France & Spain (Below)
^^^^ As you can see, I have a true friend of the Reich here ready to assist me in distracting france so I can eat it's colonies..............