A properly-fitted, well-maintained bike shop (not department store) quality mountain bike.
Your local bike shop can advise on an appropriate bike for your rider.
A properly-fitted bike helmet in good condition.
Closed-toe footwear. Bike-specific shoes are highly recommended.
Water bottle and frame-mounted bottle cage, or a hydration pack. Handlebar-mounted water bottles are not permitted.
Spare inner tube that fits your wheels and tires.
Pump or CO_2 inflator with cartridges
Spare chain master link that fits your specific chain for repairs in the field. Your local bike shop can help determine which one you need.
Bike-specific multi-tool for adjustments and repairs.
Tire levers
Front and rear bike lights
Handle bar end plugs (this is a safety measure)
Necessary medications (albuterol inhalers, epi pens, glucagon, etc.)
Team jersey (available for order at the beginning of the season)
Eye protection
A lightweight, wind-/water-resistant (but breathable) cycling shell for inclement weather
Bike gloves
Padded cycling shorts
Non-cotton athletic clothing
Frame bag, under-seat bag, or (hydration) backpack to carry riding essentials (tools, etc.)
Sufficient snacks for the planned ride (200 - 400 calories of simple carbohydrates per hour of planned riding)
Spare derailleur hanger that fits your bike
Kick stands
Bike Locks
Jeans
Bar ends
Anything that you do not want dirty