As a regular commuter, I also *highly* recommend one of the brands of Kevlar-belted tire out there. I use Conti UltraGatorskins, but I hear Specialized Armadillos and some of the Schwalbes are great, too. They won’t protect you from anything spike-shaped (I’ve gotten flats from an industrial staple and the tine of a plastic fork), but broken glass is no problem.
And changing flats on the fly really isn’t that big a deal – at least, not if you practice at home first. That first change will take you forever – and then every subsequent one will take you less than five minutes. If you travel with a spare tube you can always patch the flat one at your leisure at home.

Pumps with a fold-out foot thing like this allow you to get to ~80psi on the side of the road – so you don’t get another flat on the way home. (Or you could go with CO2 cartridges, but the pump is a bit more reliable if you are inexperienced with the cartridges.)

1) Slime sucks to work with. The day that tube dies it’s gonna make a mess.

2) You really owe it to yourself to learn and practice how to change a flat quickly. Always carry a spare tube, a tire lever, and a pump that gets you to good enough pressure to get home. You never want to be stranded in the middle of nowhere or in a questionable neighborhood with your only way home being your feet. (I would say this is particularly true as a woman – being self-sufficient is the safest option) Practice changing tires in your living room while you’re watching TV in the evening. Get as close to 5min as you can. If you don’t have quick release wheels, also carry a 15mm closed box wrench with your pump. I wrap mine up in a bandana and keep it in the bottom of my bag so I am never without.