In a non-switching, regulated power supply, with a full bridge rectifier, what can we do to minimize AC ripple within reason? Is going to a larger cap the general way that this is addressed? What are additional design considerations to deal with ripple if we can effectively negate it?
I will start with your question as asked, except for the part that goes "within reason".
First, take the case that a regulator is not used, and all ripple reduction is performed by passive devise. In this case you are restricted to passive devices which store energy, in order to fill in during the periods when the rectifier voltage is low. This means either capacitors in parallel with the load, or inductors in series. In this context, "within reason" presumably means "not too big" or "not too heavy", but this is like asking how high is high.
The second case involves using active componenets, anything from simple zener to a transistor circuit to an IC regulator. Again, "within reason" is completely undefined. Generally, you can make ripple arbitrarily small if you throw enough resources at it, and this will include part positioning, wire routing, and magnetic shielding. I've heard of commercial equipment designs which used 2 linear regulators in series.
From your comments. you're thinking about supplying power to a processor IC. In this case the answer is simple: you are doomed if try to do it passively. A regulator (either switching or linear) is the only way to go. In this case, almost any circuit you can find will suppress ripple far below what a processor will require.