I've read good things about arbor presses, but overall I don't think my reloading (or shooting for that matter) is to the point where I would notice a difference. That said, at one point, I couldn't find the seating dies I wanted in stock, so I almost went with a Wilson seating die that uses an arbor press. In that case, I think if you really want to have data on consistency, I would want the seating pressure gauge. At least as some trusted wise/experienced shooting friends (both in person and YT) have told me.
On the neck tension thing, I just try to focus on consistency. I believe (have read, been told, etc) that spring back is real, but I haven't tested differences myself. I have a -0.0015 expander mandrel and I have a range of bushings for my sizing die, but I try to stick with one setup. The different bushings were because I was shooting different brands of brass and in case I noticed a difference in the ID of the bushing itself (tolerances). I considered trying different neck tensions by varying the bushings and mandrel sizes, but I am proceeding down the "consistency is key and isolate variables" path.
Getting back to annealing, I am doing flame annealing now. But I have seen the benefits of the AMP, both my buddies and online. Again, I don't think my reloading skill or shooting is at the point where I would really notice, but anything to eliminate variables is always helpful. At least IMO.