There are many things that can be carried on a commute. There are three things you cannot do without:
1) You have to carry both an extra tube and a patch kit, along with a good, frame mounted pump which can get up to the required air pressure. Doesn't matter what type of bike/tires/tubes you use, you *will* get flats.
2) If you carry anything with you and you have a road bike or hybrid, you will probably break a spoke. This is particularly true if you use panniers. So carry a spoke wrench. Don't worry too much about carrying extra spokes; you can usually true a wheel up enough to ride with a spoke missing if you have a spoke wrench.
3) Carry some cash. This will get you a ride if something unmanagible happens.
A good multi-tool, with some allen wrenches is also handy. Zip tyes are good as well for a jury-rigged road repair.
The above is what I started with, and is enough to get you started.
BR
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Cat 2 Track, Cat 3 Road.
"If you’re new enough [to racing] that you would ask such question, then i would hazard a guess that if you just made up a workout that sounded hard to do, and did it, you’d probably get faster." --
the tiniest sprinter