I would say go with design, if not design validation (product engineering), if not that test. I pick that order because design gives you the most creative freedom which is very important in a job long term, the more monotonous the job the more you will learn to loathe it (the time it take for you to loathe it is proportional to how much of a "free spirit" you are, but you will get there). Validation / PE is generally before test while the product is still in the design phase (this is where I am at right now and as a creative person I'm goin nuts). Test is more a part of qualification and manufacturing, you check an already designed product for manufacturing defects, lots of automation stuff.
As for career paths, design allows the best gateway into an in depth technical career path, PE gives you great management opportunities, and so does test but neither of those are good for an in depth technical career path, they also can serve as a gateway to things like applications engineering or technical marketing and sales.
If you want to be a technical guy who knows a lot about the details of things and like to create, take the design job hands down, the other two run you the risk of pigeon holeing you in the wrong career path (i wish someone told me that about PE).
If you want to move towards the business end of things, management marketing sales type jobs then take the PE job, its the best way up that ladder and probably offers the best route to some very very high pay (my PE job pays very well).
Test is about the least desired job out there and you get a good view into manufacturing, so if you are interested in manufacturing and want to climb up the corporate ladder in a manufacturing environment then go with that kind of job, but IMHO opportunities here are the most limited.