Cisco switches. If you're not physically doing it, go top shelf.
Cisco Managed Switches, maybe something that even has Fiber built in that you could setup 2 switch 'closets' on either side of the building to allow for future expanding.
The thought between a 24 and 48 port comes down to traffic and really, if the switch goes bad, 48 connections drop. As opposed to only 24, but even then if that switch to connecting to another switch it drops.
You could show the difference between going with 2-24 port switches or 1-48 port switch because within IT, our budget is a huge concern for company bean counters. Very rarely do you get what you ask for when working in IT. A strong aspect of being in the higher levels of IT is budgeting and controlling costs effectively.
Now, since you're in a college of engineering and such where large files will be used, I'd recommend using fiber to connect the switches together, especially on a 48 port switch. All that data has to transfe somewhere and over Fiber would be the optimal solution.
For each department you may want to give them 1-2 48 port switches, depending on how many connections are needed (and maybe 20% extra for future expansion) and between each switch have Fiber setup. A hub and spoke setup but the 'spokes' being a fiber connection.
4 servers would not really be enough (in the real world of what you're looking to do). In knowing that you'll want to have a lot more additional ports on the network available and you want to make sure you have the bandwidth available. Fiber connections between Cisco switches is key to your project.
On top of that you would be able to run gigabit from the switch down to the computers which would be a huge benefit to the success of your network.
Here's a link to something you'd want in your situation:
http://www.cisco.com/en/US/products/ps6021/index.html
That offers fiber, 10/100/1000 and upgrades to the future 10GB network connection. That is also a managed switch which is ideal. Now, going further down the road you can also look at unmanaged switches which would operate at 10/100/1000/fiber - whatever the device using the unmanaged switch would be.
You could use a managed switch in the center/hub and put unmanaged switches out at the end of your spokes (departments). Or you could put in a couple managed switches and run lines out to each department/spoke. Either way, its all about how you want to design it. No way is right or wrong really, but in the real world it comes down to the cost.