I wouldn't try to match switch for switch based on what they have now. I would look at their needs today and then get them the right switch for their needs. The benefit you get from Extreme is that you can do security at the edge of the network based on various profiles that you want your users and devices to have.
If you are new to this concept I wouldn't try to do this without help from Extreme or someone who knows their product line very well. They have various switches that would replace the 2960s but it would depend on where you end up with your policy design. There is no equivilant to this in the Cisco world.
You can deploy Extreme with the same design as Cisco, by doing security at the VLAN interface but you are missing a big benefit of going with Extreme. If you were to do this you could replace the 2960s with B5s and the 3750s with C5s with a routing license. As for your core I am not sure. It depends on the size of your network and how many ports you need and how much redundancy you are needing. You may be able to get away with a pair of SSAs with VSB or a pair of S3s or S4s with VSB (Virtual Switch Bonding). I recommend a redundant core if you can afford it.
We just went through this same change over the past 3 years. We are a College too. Feel free to contact me directly if you need help.