Bloomer

Same as mine:

 
as you can see it's workable. As a programmer it's good practice to avoid going over the 80th column anyway, that's about the screen's halfway point at this resolution.

I'm 5 years deep in IT engineering and I use a 12.5" thinkpad x220. You'll be fine.

If you're using desktop computers mostly, then even 19 inches will be not enough. But if you're used to notebooks - it will be not so big difference. You can compare it to switch smartphone from 6 to 5.5.

That's what she said
 
To be honest, as someone who uses 3 large monitors with my desktop, I don't see it as much of an issue - of course it would be nice to have a larger screen on my laptop, but I find portability to be more important.

Since you will most likely be walking around, carrying this thing on your bag throughout your collegiate career, a 14inch notebook is enough. Your back will thank you. I had a 14inch full thickness laptop when I was in college and I wish I had a lightweight notebook instead.

You shouldn't worry about your size so much any laptop will do.

The motherboard shouldn't affect performance or cooling outside of oc'ing. Just make sure the board has any features you may want.