You may get one, but you would be very VERY unlucky to get two in a commute, depending on how far you ride.
Once you're fairly practiced at it you can get one changed in 10-15 minutes, so just set off that much earlier.
Don't put slime in, it doesn't work very well and probably adds quite a bit of weight.
Just get some good tyres, but do pay some attention to other properties of the tyres, such as rolling speed, grip, weight, etc. not just puncture protection, I did this and got some specialized armadillos and didn't like them that much. Replacing them when they start to let punctures in is more important than getting the 'most puncture resistant' ones in the shop in the firstplace. Remember, OLD tyres are far worse than BASIC but new tyres.
And, without wanting to be condescending, most of them are only biddies off to the bingo or post office, or schyoo-dents on their way to the fish and chip shop (with cheque books at the ready due to having spent their entire week's loan allowance on fags and your fare), so I wouldn't worry TOO much if you're a bit late.
But I never really understood the logic of commuting TO a job where you then drive ROUND all the time, probably covering many times the distance of your commute. I know you can't, but it just would seem more logical and efficient to me to park the bus at your house and just set off from there.
edit: oh, another point - make sure you can get the tyre off the lever without too much effort. If you can't do it, you're not going to be able to recover from a puncture very well, so it's as bad as not having any puncture repair equipment.