A HeNe laser is far superior to a cheap laser pointer for several reasons:

• The discharge and mirrors are clearly visible permitting the lasing process to be described in detail. Compared to this, a diode laser pointer is about as exciting as a flashlight even if you are able to extract the guts.
• The beam quality in terms of coherence length, monochromicity, shape, and stability, will likely be much higher for the HeNe laser should you also want to use it for actual optics experiments like interferometry. (However, the first one of these - coherence length - can actually be quite good for even the some of the cheap diode lasers in laser pointers.)
• For a given power level, a 632.8 nm HeNe laser will appear about 5 times brighter than a 670 nm laser pointer. 635 nm laser pointers are available but still more expensive. However, inexpensive laser pointers with wavelengths between 650 and 660 nm are becoming increasingly common and have greater relative brightness.

The HeNe laser assembly from a barcode scanner is ideal for this purpose. It is compact, low power, usually runs on low voltage DC (12 V typical), and is easily disassembled to remount in a demonstration case. The only problem is that many of these have fully potted "brick" type power supplies which are pretty boring to look at. However, some have the power supply board coated with a rubbery material which can be removed with a bit of effort (well, OK, a lot of effort!). For example, this HeNe Tube and Power Supply is from a hand-held barcode scanner. A similar unit was separated into its Melles Griot HeNe Tube and HeNe Laser Power Supply IC-I1 (which includes the ballast resistors). These could easily be mounted in a very compact case (as little as 3" x 6" x 1", though spreading things out may improve visibility and reduce make cooling easier) and run from a 12 VDC, 1 A wall adapter. Used barcode scanner lasers can often be found for $20 or less.

An alternative is to purchase a 0.5 to 1 mW HeNe tube and power supply kit. This will be more expensive (figure $5 to $15 for the HeNe tube, $25 to $50 for the power supply) but will guarantee a circuit board with all parts visible.

The HeNe tube, power supply, ballast resistors (if separate from the power supply), and any additional components can be mounted with standoffs and/or cable ties to the plastic base. The tube can be separated from the power supply if desired to allow room for labels and such. However, keep the ballast resistors as near to the tube as practical (say, within a couple of inches, moving them if originally part of the power supply board). The resistors may get quite warm during operation so mount them on standoffs away from the plastic. Use wire with insulation rated for a minimum of 10 kV. Holes or slots should be incorporated in the side panels for ventilation - the entire affair will dissipate 5 to 10 Watts or more depending on the size of the HeNe tube and power supply.

When attaching the HeNe tube, avoid anything that might stress the mirror mounts. While these are quite sturdy and it is unlikely that any reasonable arrangement could result in permanent damage, even a relatively modest force may result in enough mirror misalignment to noticeably reduce output power. And, don't forget that the mirror mounts are also the high voltage connections and need to be well insulated from each other and any human contact! The best option is probably to fasten the tube in place using Nylon cable ties, cable clamps, or something similar around the glass portion without touching the mirror mounts at all (except for the power connections).

Provide clearly marked red and black wires (or binding posts) for the low voltage DC or a line cord for AC (as appropriate for the power supply used), power switch, fuse, and power-on indicator. Label the major components and don't forget the essential CDRH safety sticker (Class II for less than 1 mW or Class IIIa for less than 5 mW).