The colors are much your choice, but my personal favorites are:
PY110 Indian Yellow
PY129 Azo Green
PY184 Bismuth Yellow
PR101 Transparent Red Oxide
PR254 Pyrrole Red
PV19 Quinacridone Rose
PB27 Prussian Blue
PB60 Anthraquinone Blue
PW6/4 Titanium White
Just oil (I like walnut oil, it's nice and slippery) or oil mixed with calcium carbonate (or fumed silica).
Oil followed by soap and water.
For the last 2 you can see my video on how I Rinse the Brush with Oil
. After doing that I just wash the brush with soap and water.
In the studio I keep my brushes suspended in oil as shown here but without ever washing with soap and water. Years of suspension in oil for several of my brushes:
I have actually cleaned both my jar and my oil since that picture:
Notes: Oil works to thin the paint to the desired consistency, do not use tons... Oil paint shouldn't ever be watery thin (or in this case purely oil thin). Oil can work as the only medium in layered or alla prima paintings, when working in a layered approach be sure to either allow the painting to dry well between layers (keeping each layer thin), or add a little oil to the top most layer of paint and keep layers about the same thickness overall. Generally speaking glazing over thicker passages of paint will cause more likelihood for cracking after some number of years (if longevity of the artwork is a concern).
Walnut oil dries a bit slower than Linseed oil, both in the paints and as a medium used for thinning the paint to the appropriate consistency. Anything used to adjust your paints should be used sparingly for the most part (I break my own rules when using my extender... it doesn't thin the paint just changes the ratio and types of solids).
My extender is the same stuff I use for my medium, oil mixed with calcium carbonate. I get the calcium carbonate in the form of Marble Dust, bagged and sold by Fredrix (the manufacturer of good canvases and other painting surfaces). A 4lb bag costs less than 10$ US and it lasts for ages, making my extender is just a matter of mixing the two together, tiny drops added to a pile of marble dust and worked together with the palette knife. I will make a video on this at some point. I use it in a variety of ways, just using oil is also a standard for me as medium or thinner.
Regarding Olive Oil for cleaning brushes: Yes you can use it, but be sure to thoroughly rinse it out of the bristles and allow to dry before using paint with it. You do not want large amounts of Olive oil in your paint, it will take ages to dry and may compromise the integrity of the paint film once dried. I personally feel my method for rinsing a brush to be better and keeps the oil cleaner and wastes less over time. Also, by using Walnut oil for rinsing the brush you do not have to concern yourself as much with the paint film not drying properly.
This about sums up painting solvent free. There are other ways to work as well, the paints I use are either M Graham or ArtTreehouse paints, both made with walnut oil. They are very smooth paints and handle beautifully together, I find them exceptionally pigmented and worth every penny.