First off I don't think you need a cross bike (although they are nice bikes).

My suggestion really depends on your budget. Since you will be commuting to school you will also need a lock and/or a rack & bags in addition to the tires. The tires should be good puncture resistant tires like the Schwalbe Marathons, Panaracer Ribmos or T-servs, or the Specialized Armadillos. The lock should be a decent Ulock like the Ongaurd Bulldog or Kryptonite Evolution series. You may also think about adding bar ends to your MTB to get more hand positions.

Also if you can afford it, there is nothing wrong with having a 2nd bike. Those mid 70's to 80's bikes you posted look like ideal candidates.