I've never drawn with Photoshop so I can't recommend brushes, but I hear that Lazy Nezumi Pro is a pretty popular companion program since PS doesn't have a built-in stabilizer.
For imitating traditional art, to speak broadly, it basically comes down to finding the right blending/dilution/persistence settings to mimic the spread of the type of paint you have in mind. For cartoony art, you'd just reduce or disable those three settings so that you get flat colors without picking up the paint underneath. Photoshop might use different terms for those three options.

there is also a free art program named MyPaint, which imitates a lot of traditional medias from pencil to watercolour, oils, acrylic, charcoal, wiping finger... there are layers, but you can't manipulate it photoshop style. like in real life. :)

another program I sometimes use is FireAlpaca. looks like a mix of photoshop and Paint Tool SAI, has only limited brushes (but somehow enough to get art done IMO), no structure effects, but can handle a lot of layers, runs stable, and has an inbuilt perspective tool.

as for shaky lines, if there is not a tremor you have to deal with, try to learn to handle the stylus with a light hand. or ignore the shaky lines. XD

Some of these smooth lines are achieved through technique (by building up from many small, tapered lines along the length of the curve), but stabilizers can be used to draw these lines in a single stroke. Painttool SAI has a built-in stabilizer tool with a range of intensities. Photoshop does not, but I've read there are plug-ins for it. I couldn't really say which brushes work -- this is something I'm still trying to figure out myself.