From what I've been told, washing is useful because the molds are coated with a chemical that helps release the styrene from the mold once it's cooled off. Some paints react with the release chemical. It's not mandatory--I built models for years without washing them, and even now most of the time all I do is brush on some common isopropyl alcohol and let them dry.
The toothpaste thing I haven't really heard about.
The tools I use:
A good set of wire cutters or toenail clippers. Useful for taking the parts out of the sprues--twisting them to release them can leave some ugly scars.
An Exacto knife for slightly bigger part cutting.
Some people swear at it not by it, but Testor's non-toxic cement, the one in the blue tubes with the lemony scent. The stuff in the red tubes is more toxic, stinks even worse, but sticks better--but the blue stuff has been more than effective for me. The Polar Lights ECTO-1 is a snap-fit, so it doesn't require glue, but the AMT ECTO-1A will.
I prefer to use acrylic model paints, which are water-based; Testor's Model Master line most often. I do have a set of acrylic "paint pods" that is useful if I have, for example, one tiny little part that's suppose to be green but it's not really worth buying a whole new bottle of paint for.
Heck, this is the exact thing I have right here:
http://www.testors.com/product/0/9186/_ ... _18_Colors Enamel paints are oil-based, and thus harder to clean up. I know modellers that insist that they look better, and maybe they're right, but the easy of clean-up and not having to deal with foul-smelling thinners as much more than makes up for it with me. The only enamels I use are for metallics, like aluminum, silver, gold, chrome, copper, etc, because metal acrylics are too watery and thin. An ECTO-1 has some chrome sections; it might be a consideration.
Brushes, it's good to have some small brushes for tiny details, and some large ones. I personally buy multiple sets of cheap brushes available at any hobby store or even retailers; I use one with the acrylic paints, and the other with the enamels when I have to use them. (I build a lot of spacecraft, so aluminum, gold, silver, etc do get some use)
There are other people who get more exotic, with spray paints and airbrushes, but those aren't really my bag.