You can create and save a Tool Preset for any tool. This will remember settings that you choose. Presets for brushes are much more useful than for some tools. If you wish to use presets, you have the option of either creating a tool preset or a brush preset. Right click on the Tool Presets button to reset the tool to default settings.

Brush Presets is similar to the following 2 panels; Brush Settings and Brushes.

Here you can change size and hardness and select from a range of brush presets. There are many brushes available and you can also create your own.

Note that this panel is very similar to the following 2 panels.

There is quite a bit of duplication in these Panels. Many things you can do in either, although the Brush Settings Panel has more options.

The Panel contains 2 tabs; Brush Settings and Brushes.
This is the Brush Settings Tab.

This panel allows you to customize any brush with a wide range of options and settings, which will change the characteristics of the brush. You can then save these brushes.

Brushes You can access a vast number of brushes, search for particular brushes and more.

Brushes are a very large subject, too large to fully go into here, but I will write more on them in the future.

As mentioned in the previous option, there is some duplication with this panel and Brush Presets and Settings.

Choose to paint with a range of Blend Modes, for different effects.

Change the Brush Opacity that you paint with. The next option allows you to override this if you have a pressure sensitive pen and tablet.

In one brush stroke, no matter how many times you go over the same area, the ink applied will be limited by the Opacity. If you end the brush stroke and begin a new stroke, it will apply more ink.

Opacity is often confused with Flow, (see below). Flow allows you to build up the ink applied in the same stroke, by going over and over an area.

If you have a pressure sensitive pen and tablet, if you turn this on, the opacity will be controlled by the pen and tablet. If the setting is off, opacity will be controlled by the Brush Opacity setting (the previous option).

As you paint with freehand brush strokes, choose how much Photoshop will automatically smooth out those strokes, so they are not jerky.

There are also several options.

One thing to note is that the default setting is 10%. The lower the percentage, the more responsive the brush stroke. This will also depend on your computer, processor, memory and graphics card. As you increase smoothing, you may notice some lag.

If you have a non round brush, you can change the angle of the brush.

It won't make any difference on a round brush.

Photoshop's Tooltip says "Draws Background Color over Foreground Colors". If you are painting on the image, you won't see any difference.

If you are painting on a Layer Mask, normally painting with black masks (hides) and painting with white shows, reversing where you have masked.

If you select Auto Erase and paint on a Layer Mask, it will mask with both black and white. To be honest, this is useless. If you want to mask, use the Brush tool and paint on a Layer Mask with black. You then also have the opportunity to paint with white to reveal areas, if you wish.

If you have a pressure sensitive pen and tablet, you can turn on this option, so brush size is controlled by the pen pressure. If this is off, size will be controlled by brush settings.

For non pressure sensitive users, the best way to change brush size is with the square brackets keys [ ].

Paint symmetrical patterns and shapes with this option turned on.

There are a number of symmetry options available.