Certification Foo

So, my teacher and another computer teacher for my school both claim that I don't need to get my A+ or Network+ certifications now that I have Linux+. Their advice is to go for a CCNA next. I kind of have a feeling they're wrong, and that while the CCNA would be good it would look better overall if I had all three. (Plus whatever else I can get, I'm thinking RHCE and LPIC potentially.) You guys are actually out there in the field, what do you think? If my teachers are right, it could save me a bit of cash and effort. If they're wrong, I'd rather know about it now than a few months into a jobhunt with just a Linux+ cert under my belt.