Concrete is cheap, don't scrimp. A quality chain link fence will last for years, but not if you don't sink the poles appropriately. Freeze Thaw cycles, wet dry cycles, a good windstorm, several teenagers jumping over it, etc all will serve to weaken the concrete to ground connection. Your post holes should go at least 2 feet deep, if not deeper. Rent a one man auger (it comes on a cart with the motor on the wheel end and the auger on the handle end about 4' long. Much easier than a freestanding auger!) and go for it!
The thing about chain link fencing is that it doesn't like to bend over the contours of hills and valleys very well. This is where a more flexible type of fencing like cedar board fencing really has its advantages. Chain link has a shear factor that is hard to deal with in extreme elevation changes.
As far as straightness, buy some builder's string and string it top and bottom along your fence line. You want to set your posts so that they just barely touch the string without deflecting it. Make sure the upper and lower strings are exactly "level" (the one is directly vertical of the other) so that your posts are level. You can buy a post level that levels in 2 directions and secures to the post with rubber bands for about $5. They work pretty well.