The choice of which 4th axis carving strategy to use - indexing or continuous - depends on the configuration of your part and your expectations for it. To use your rifle stock as an example, if that slot in the top of it needs to be square on the sides, then an indexing strategy would be best. If you carved it using a routine where the tool moves down the X axis, increments in A, then moves back up to X zero, etc. then your slot would be wider at the bottom than at the top. But if your primary concern was smoothness on the outside, you could use the continuous strategy and put in the slot later, as a separate operation. Indexing usually will show a little discontinuity where the various toolpaths meet.
For jobs like this where you need a smooth contoured surface, a ball-end tool is always used. Otherwise you'd have gouging from the edges of a flat endmill. It does remove less material at a time, though. 3D carving is always going to be slower than 2.5D. The cusps where the passes of the tool adjoin are smallest when the diameter of the tool are largest and more noticeable when the diameter is smaller. To counter that tendency, you need to space the step-over tighter with smaller tools. But it's not in the millions even then; an approximately flat surface can be achieved without infinitely small step-overs. Since your rifle stock has a generally smooth surface without tight spaces that need to be reached by the tool, it looks like you could do the whole thing with a fairly large-diameter ball-end cutter, like about half an inch.
I'd suggest using DeskProto as your CAM package; it can do both types of 4th axis carving - indexed ("n-sided") and continuous (along X or along Y), and has a lot of other handy features as well. We sell the multi-axis edition at a significant discount to hobbyists. I don't know of any books that talk about 4-axis carving in any depth, but there's a lot of instructional material on the DeskProto site: DeskProto offers CNC machining for non-machinists