You can simulate a transmission line with lots of series inductors and parallel capacitors, but that is a lot of trouble and I'm not sure will give you the insight you really want.
It's actually not that hard to see obvious transmission line effects at high frequencies if you have a oscilloscope. If your electronics club doesn't have one, that would be a great piece of equipment to ask for. In the mean time, find some company in the area that does electronics and is willing to help out high school students. I suspect most of them would be happy to help if asked.
We did this in a lab in college, and I remember being surprised how clear and obvious the results were. Get a spool of some cable. Coax would be great, but 100 feet of ethernet twisted pair cable will work well too. Most likely whoever handles the network in your school has a spool of "CAT5" or similar cable they can let you borrow.
Use a signal generator or a simple circuit with a digital output that makes a square wave. Connect ground and this square wave to one end of a twisted pair, and get access to the other end of the same twisted pair.
First just look at the signal as injected at the transmitting end with and without about a 50 Ω resistor in series. Especially with the resistor, you should be able to see stair steps as the reflection from the other end gets back to the transmitting end. Now you can put a 50 Ω resistor accross the far end and see the effect it has on the transmitting end. Also look a the signal at the far end with and without each of the resistors in place. I think you'll see clear artifacts from the reflections, and how things quiet down but are half the voltage with the resistors in place.
Other things to do is to adjust the resistors for minimal ringing, which means finding the characteristic impedance of the line. It would also be a interesting exercise to measure the total propagation time thru the cable, measure the length of cable, and compute the actual propagation speed on that cable. You may be surprised what you find.