I use a converted fixed gear with fenders and brakes but I bought my daughter a Specialized Globe internal geared 8 speed.
It cost a bit but it’s a great bike, a bit expensive but if you pencil out everything I think it’s a good deal.
8 speeds and no deraileurs to adjust or get banged up in a bike rack.
Perfect chain line.
comes with fenders, rear rack, step through frame, generator front hub with front and rear lites, 700 wheels with reflective sidewall tires which are fairly wide.
Canti brakes (disk would have been nice)
I go about 1.5 miles each way on an older c’dale CX frame I picked up. I have it fairly upright, the Headshok gives a bit of suspension, and the CX tires help take the harshness out of some old road wheels I had lying around. There are eyelets for rack/fenders too. I just use a plastic fender than attaches to the seatpost, so the eyelets could be used. I too use a backpack- some days I’m hauling 30# of books and lunch. I’d advise going the cheap route b/c a LOT of folks who ride sometimes have heavy, cheap bikes that they don’t care for that well, and throw them on the rack without paying a lot of attention. Hate to scratch up a new frame!