I would have the club
I would have the club provide a simple inexpensive and expandable robot kit that they sell to the members. I like this one for the chassis (it was one of the one’s ossipie’s choices).
Another choice is the Dagu Magician chassis for around $15. I got mine from SparkFun, plus about $10 for the encoders.
It would probably be best to have a single controller supported by the club for the beginners at least. My favorite is the Teensy 3.1. It's $20, but it's about the size of an Arduino Nano, is programmed from the Arduino IDE with a simple extension to the IDE. It has a large amount of pins, but to access some of them you need to put headers on the top. The Teensy 3.1 is running an ARM Cortex-M4, with 256k flash and 64k of RAM. There are built in level shifters so you don't have to worry about your voltage mostly.
Another choice for the controller is a Raspberry Pi for around $35-$40.
I'd return to eBay for sensors and motor controllers. There are SRF-04s for a couple dollars per and lots of other things you can make IR distance sensors from.
Unfortunately the cost can add up quickly, so I won't suggest that robotshop.com has the Hokuyu laser rangefinders.
If, in addition to the money that each member brings in through dues or an initial purchase of their bot, the club might get some money of its own to buy some more expensive items like tools and solder and some basic components. And don't forget a few GPS units and other interesting sensors that individuals might not be able to afford but the club could loan them for a while to a member with a good idea.
It takes imagination and discipline to make robots on the cheap. I like using 8020 aluminum extrusions for the skeletons of my larger bots and OpenBeam for the smaller ones. These don't seem cheap at first, but you can use them to avoid welding.
Another extremely useful tool is a 3d printer. Print your own chassis design if you have design skills and imagination. Even if you don't want to print the entire thing you can still print the connectors and joiners. I'm hoping to be able to print motor mounts for Bilbo (an unknown Marx brother) because I don't have metal working tools and the motors were from eBay with non-standard mounting points.
If you can and know what you're looking for, search for motors everywhere. Garage sales and eBay and Craigslist and Goodwill and suchwhat are wonderful places to spend time.
Have a nice day, and happy building!