Updated: Feb 1, 2021
This is the list of what I consider the materials necessary to paint in oils. This is not a list of basic materials but rather a comprehensive set with some tips as to why you need certain things.
Use glass! Since I found out this secret my life has changed. Glass is so easy to keep clean properly, it allows you to tone it from the other side so that you can see your colour properly.
You can clean the palette with odourless mineral spirit such as Gamsol and kitchen paper with ease. If the paint has hardened you should use a stanley blade to scrape it off, it will bring your palette back to life no matter how hard the paint became (but obviously try not to get to that point!)
Glass jars with tight fitting lid - you can never have enough of these. Have 2 basic sets: small jars where you can mix your mediums, and biggish jars where you can put your Gamsol. The Gamsol jars are to clean your brushes and you palette of course: have a minimum of 2 of these jars: the first to use as the first dip of your brushes, for the paint that you cannot get rid of with the paper towel, the second jar to use after you cleaned your brush as much as possible using the first jar. You will notice that in this way your brush will be totally paint free.
The major rules to chose a jar are:
tight fitting lid but never use a lid with a rubber ring or a plastic lid (I learnt from experience: a rubber ring will become brittle and will stick to the jar, making it impossible to open!)
a round bottom: avoid corners even if wide as your brush wil find it difficult to reach the recesses.
For a canvas of 30x40cm (or 20x30) I use Filbert brushes size 4, and I have at least 4 of these at hand for different colours and especially for different values; I also use the smallest Round brushes size 2/0, and again I tend to have at least 4 around. For foliage I use the corner of a Fan brush - again quite small (size 1 and 0) and I have at least 2 at hand. I buy my brushes at https://www.rosemaryandco.com/ .
Take care of your brushes!
When cleaning the brush on your paper towel always pinch the brush and pull it out of the pinch, never wiggle the brush on the paper. This is your main golden rule.
Also try to keep them clean between sessions:
If you use very fat mediums you can leave the brush full of colour (don't clean it with a paper towel) for a day.
In all other scenarios (not a full fat medium, more than one day, etc) you need to clean your brush properly: paper towel, Gamsol, paper towel, Gamsol again and eventually the clean Gamsol jar.
Do yourself a favour and never ever leave your brushes dirty, you would have to leave them in Gamsol overnight (and you DO NOT want to do that, as the bristles will lose shape entirely) and even worse, DO NOT leave them in soapy water overnight - if you do, you may as well throw them in the bin directly.
An excellent review of paints is this one: https://jeffchester.wordpress.com/2013/05/23/24/
A good brand is Winsor Newton Oil Colour paints. A better one is Winsor Newton Artists Oil Colour. I lately use Geneva paints: https://genevafineart.com sold in the US, or distributed in the EU from the UK.