Multi-tool, flat repair kit + tube, full coverage fenders, decent blinky lights for front and rear if riding near sundown/sunup, a good luck charm, and slick tires if the bike has knobs.

I recommend a Radbot 1000 and Planet bike 1 Watt Blaze for cheap but very bright lights.
vittoria randonneur are my favorite tires at the moment for commuting.
Serfas fenders from amazon are cheap and of decent quality, SKS Longboard fenders are probably the most effective.

A rack and panniers is nice, but a book bag works just fine. The cheapest way to get weight off your back is to get a rack, bungee a bread rack to it, and bungee a back pack to that.