There are several different ways demonstrate quantum mechanics, depending on what your class is like and what you're trying to demonstrate.
Do what Einstein did
Black-body radiation is the light emitted by a hot object. Over a hundred years ago, Albert Einstein and Max Planck used black-body radiation and statistical mechanics to demonstrate that light is quantized into photons.
Under the Classical Theory of Radiation, every hot object emits the same color spectrum of light. When you increase the temperature of an object the quantity of light would increase but the color would stay the same.
But that's not what happens. When an object gets hotter its peak color changes. This is a result of statistical quantum mechanics. In fact, it was this experiment which helped us discover quantum mechanics in the first place, long before experiments with expensive things like lasers.
Different temperature objects emit different spectra because higher-frequency light has more energy per photon than lower-frequency light. Basically, an object can't emit any high-frequency light at all if its temperature is too low. Therefore changing an object's temperature changes the frequency distribution of its emission spectrum. If light wasn't quantized then every object could emit low amplitudes of high-frequency light.
So light a fire (or just buy a butane lighter). Examine how the hotter parts of the fire are blue and the colder parts of the fire are red. The color difference doesn't make sense unless light is quantized.
This kind of experiment shows how much scientists have discovered using cheap, simple tools.
For a little more money you can buy an \$11 spectroscope. Use it to look at things with clear emission lines like a pure neon light or a computer screen displaying with a solid primary color rectangle. (It might take research, experimentation and additional purchases to find light sources with clear emission lines.) The light will split into clear lines instead of the continuums you'd expect from the previous black body experiment. These emission lines correspond to electrons jumping from one quantized energy level to another. In particular, they correspond to pairs of different values of $n$ among the electrons' quantum numbers.
This experiment is good because it lets students see the quantum numbers directly. If your students are good enough at math they might even be able to figure out which $n$ jumps the lines they look at correspond to.