If you don't do any gaming an ultrabook is definitely the way to go, trust me when you have been carrying a laptop to class all day the lighter weight and better battery life will really pay off.
I was told I would need 8 gb of RAM and at least 250 gb of storage to be able to handle thr classes I would take in computer engineering. Is this true?
8gb of ram is useful however the 250gb of storage is a completely arbitrary number someone picked. The ThinkPad x220 I used for college (CompSci major) has a 120gb SSD and that was plenty of space, you can always get an external hard drive if you need it.
If you do want 8gb of ram I would go for the Dell XPS 13, it isn't as popular as the other models but I have used them at work and they are fantastic systems.
The Dell Online Store: Build Your System
Be sure to get the 1080p screen too, it is well worth the money.
If possible, I'd recommend storing homework and projects on some sort of cloud service, such as Dropbox or SkyDrive. It keeps your files secure, and you don't have to worry about losing them if your computer's HDD crashes or something similar happens.