So yesterday before I leave for work I top off both my tires. They take 45-65 psi and I inflated both to 60 psi. Everything was fine on my ride in, I get five minutes into my ride home and notice both tires have gone flat (front is just too low too ride on back is truly flat). The end result us my having to walk five miles home.

I just replaced my worn out tires with these about two weeks ago: Schwinn Bike Replacement Tire...
and they're paired with Schwinn self-sealing tubes.

Now, I still need to see exactly what caused this set of flats. (I was seriously too frustrated last night to deal with it by the time I got home.) But what's everybody's advice on a decent "Iron tire" type setup? Also, would going tubeless help prevent the near constant flats of commute city riding?