I really wouldn't stress learning Teamcenter at all, the company I work at doesn't expect new hires to know anything about TcE and there's a lot of on the job training available out there. As far as NX, I'm a daily user and more than anything else I'd advise getting in and getting your hands dirty. I don't know what student licenses are available for NX but I know your time spent in more accessible programs like Solidworks would be well spent, the two programs share a lot of code and have very similar work environments. The best thing you can do if you want to get better at CAD is start working in it, build models, mate assemblies
omegle voojio, and produce buildable drawings