A beginner's list of sure-fire aquarium plants
A starter set of guaranteed plants would consist of: Java Moss, three ferns — Java Fern, Bolbitis and floating or plantable Water Sprite — the irrepressible floating Duckweed, Hygrophila, Echinodorus — the "Amazon Swords" — and the slow-growing Anubias barteri, both in its regular form and in a dwarf form called Anubias barteri nana ("nana" just means "dwarf)." There's no mystery to growing these plants, in water conditions that vary from strongly acidic (pH 6.4) to somewhat alkaline (pH 7.8).
These plants, with a very few others, are what you'll find in the following pages in the menu on the left.
In New York's soft water, the carbon plants require is available as dissolved carbon dioxide, not locked up in carbonates, as they are in hard water. This makes planted aquaria easier to maintain. In harder water than mine, the list would be different; it might include Hornwort (Ceratophyllum) and Vallisneria, which rot away in soft water. There are Cryptocorynes suited to hard water as well as soft water.