Sorry about your wallet!
Still, there are few necessary accessories.... just those that are useful.
I carry a good repair kit and two spare tubes, though I rarely get a puncture.
I carry a lock, though I dont need to lock my bike up at work or at home, and dont generally stop on the way.
I like glasses, but have ridden without them.
I sometimes have worn gloves in summer, and do so currently, but have often not worn them.
I have good winter gear, but then it gets down to freezing here, and I ride year round.
I buy a computer for my bike whenever I buy a new bike. It doesnt leave the shop without one, but then I am a numbers geek.... your km-age may vary.
z