One Question/Answer that everyone should read is: How do I learn Unity fast? It contains a ton of tutorial links, videos, book recommendations (Will Goldstone has a book on Unity Game Development that's great), etc.
for game logic and drawing GUI i recommend simple 2d shooter tutorial at 3d buzz, you can use OnTrigger colliders for collecting objects ( increase score and delete object you have collided with).
for making games you wont need to go study university level programming carreer as I did, you only need passion and dicipline to learn things yourself, find tutorials online theres more avaible than you could ever do. And the more you study the more you learn.
My motivation comes from this idea that i have. This is the coolest job there is out there,
and secondly I have always wanted to learn how the games work and how to modify and make them.
Some news on Learning Unity, from the official site -