Many, if not all, of the software applications that I support DO NOT recommend Realtek NICs. I support database applications that assist in business management and Realtek NICs have been known to cause database corruption. I suspect that others will come across this same problem.
If you are not going to use some serious app that utilizes school data, I would not worry about it. The IT department has to support a lot of computers and they try to limit the products that you use therby decreasing the amount of products they have to support. Try it before you buy another.