Origami is really a great thing ! You can do loads of stuff with origami >w<
Sooo, the best is to fold the paper and then reinforce the fold with you nail. That way the fold won't open too much and the origami will look neat and clean. You can use regular paper, but use preferably special origami paper, they are already cut in a square shape, they are thinner and you can find different colours or prints. I heard about Hello Kitty origami paper, and one of the best is the pearly origami paper.
Be careful with the special fabric-like origami papers, even if you fold with the nail, the origami won't remain flat. If you want a flat origami, put it in a heavy book and wait for it to be flat. It's what i usually do with origami swans.
Also, with modular origami, be sure to use regular paper, not too thin, not too thick. If it's too thin the pieces will get very loose and will fall apart (like from the top of your modular) and if the paper is too thick the pieces won't have any flexibility and the paper will tend to tear. You can use coloured paper, or white paper, depends on what you want...
