Wool, polarfleece or polypro sweater/shirt and light pants, shorts or a swimsuit to wear under a wetsuit. Cotton will not be appropriate!
Old sneakers you don't mind getting wet (see neoprene booties remark below.) Wear wool socks inside these, not cotton! Tuck shoelace loops and ends completely under the crossed-over parts of the laces between the eyelets, since loose loops could get caught inside your boat and trap you in the boat during a capsize!
The club provides wetsuits and drytops, but not waterproof foot and head gear. Neoprene booties are a good investment for keeping your feet warm, but consult with experience boaters before buying, since there are conflicts between sturdy soles and tiny boats. For winter paddling or if you are upside down a lot, a thin neoprene hat or hood will keep you warmer, and these also come in several different types that you should research and discuss.
A large towel is a good idea, and can be used as a "Modesty Shroud" while changing by the shy or those who don't want to rile up the locals.
Money for gas. Exactly how much depends upon the distance of the drive, the number of riders contributing, etc. If you have doubts, ask the driver what seems fair. (Remember, dragging boats around also makes for a significant amount of wear and tear on a vehicle, which can be more costly than fuel. For most drivers, insurance, maintenance and depreciation cost more per day than gas, so you should not expect to pay only for the exact amount of gas used if you do not have a car to offer.) Drivers of big pickup trucks that carry lots of gear but also suck gas should get a buck from non-passengers as well.
Often we stop for food on the way to or from the river. A meal, or money for a meal, is a good idea.
Food and water for the river. (Bad things happen to dehydrated, hypothermic boaters.)
A raincoat. (The river gods always rain on beginner trips)
A full set of warm dry clothes, separate and independent of what you are wearing on the river. The clothes that you wear in the car on the way to the river usually count for this.
For the nasally challanged, nose plugs.
For the ear canal challanged, ear plugs.
Waterproof flashlight. (Useful if dark at the take-out or if the trip falls behind schedule.)
Chocolate for the trip coordinator(s). (This is optional, of course, but it is in your interests to make sure that your trip coordinators like you, you get rescued quicker and you get invited on more trips that way, just ask Tiana.)
A vehicle with racks suitable for carrying boats is often very helpful. Sometimes, a car without racks, is useful too.