Well, I'm not sure how it works in the 'States but in Canada we have a national certifying body for the machinist trade. I'm mid-apprenticeship right now on the way to my ticket, so take my opinion for what you figure that's worth.
There is alot of 'bah-humbugging' of CNC machining, but it IS the present and the future of machining. There are many, many parts that would take many, many times longer with a manual set up. Having said this, there are nearly as many parts that CNC is total overkill for. They both have value, so you should try to find a place to work that has both types of machines and is willing to train you on them. There is nothing like holding the wheels and feeling a tool work for generating an understanding of what is going on.
As for CNC jobs to avoid... none. Take anything you can get and learn what you can! If you find that the job you have is no longer challenging you, either ask to move machines or find another shop. every chip made is a lesson you can learn.
edit: the most important thing I've found is a shop that welcomes progress. Always doing things the same way doesn't yield progress. They should be willing to let you experiment to SOME degree. New/different tooling, varying speeds, feeds and depth of cut, changing clamping etc can all yield big improvements in productivity. Always strive to make it better, faster. Course, the guy before you has probably looked at alot of ways for that so ask first before you change things :)