Will I damage a plastic bowl with a marble pestle

There are at least three potential downsides:

1. wood is quite light, so you will not get the benefit of added weight of the pestle for crushing;
2. many wooden mortars have a smooth texture, which will not aid in the grinding as much as, e.g., a coarse ceramic mortar; and
3. wood is porous—increasingly so as it dries over time—so it may have the tendency to pick up the flavors of its contents.

For your average mixing task, pretty much any bowl (of the right size, shape) will do. Also, "plastic" isn't one material, it's a bunch of different materials. For example, some advantages of polypropylene bowls do not apply to melamine formaldehyde bowls, but both are plastic.

So, here are some advantages of a polypropylene (PP) bowl over a metal bowl:

• microwave safe
• high elasticity (can be bent, and will go back to its original shape. E.g., if you drop your PP bowl, it won't dent)
• extremely acid-resistant
• extremely resistant to other chemical attacks (e.g., will not corrode)
• plastic bowls are often made in a mold, so can be cheaply made in a variety of shapes. You can get bowls with nice pouring spouts, etc. because of this.

Of course, they have disadvantages too:

• fats stick, almost impossible to remove all traces (a problem when beating egg whites)
• can't be used over a pot as a double-boiler
• can't hold very hot things (e.g., you can put hot oil in a metal bowl, but PP would melt. Different plastics have different melting points, some can't even hold boiling water. You never have to worry with stainless.)
• can't be used in the oven

And there are things which are just different, like metal conducts heat better (so it works better when cooling in an ice bath, but also you're much more likely to get burnt on it), metal is denser (PP floats, metal doesn't).

If you get metal bowls, except for a few applications where copper is nice (those egg whites, again), you want stainless steel. Stainless is fairly resistant to acid and also corrosion (plain steel is not). Note that stainless comes in different grades, which vary in their corrosion, rust, and acid resistance.