For pretty much any engineering degree, you will have to take Math 112/113 (Calculus I and II) and Physics 121. Electrical will also require Physics 220. Those will provide the math and physics foundations that engineering degrees generally build off of.
As far as lower level engineering courses that may be useful before you actually enter a major?
ME EN 101 - Static Systems in Mechanical Engineering
EC EN 220 - Fundamentals of Digital Systems
CS 142 - Introduction to Computer Programming
CE EN 101 - Introduction to Civil Engineering
Also, the Mechanical and Electrical Engineering departments also have a "New Student Seminar" course (ME EN 191 or EC EN 191 respectively) that give a basic overview of the engineering programs that could be useful.