Yes, a properly fitting helmet should be comfortable and not really noticeable. Different brands (and different models) are built for differently shaped heads; you really need to go physically try on helmets to find the proper fit.

As mentioned, from the purposes of protection you're essentially the same with any certified helmet. What people pay for beyond the basics is fit, weight, aesthetics, and aerodynamics. For your purposes the first is worth paying a little more for, I find the sized helmets fit better than the one-size-fits-all, but that's because I wear a medium. Someone who wears a larger helmet may be perfectly fine with a one-size-fits-all as its starting out closer to his size.

How much to pay? I'd say you can get a good fitting comfortable and well rated helmet for $40-70 for your use.