Don't know if I can offer much here, but I looked at all-thread once for a structural application. I would be concerned about buying just any all-thread as a lot are just some sort of mild steel, and their mechanical properties can vary quite a bit. If you get something like B7 all-thread, I think you can have more confidence in it's mechanical strength.
As far as sizes go, it's probably best to look at other similar components that have proven to work well. The actual loads in the 3-link may be difficult to calculate so empirical data may be the best way to go (my guess is you're on the right track in the sizes you indicated). My Rovertym adjustable rear links have 3/4" threads (probably just mild steel), and they seem to work fine (although these are relatively lightly loaded). I'd probably look at some fairly stressed applications to see what people are running (a 3-link failure could be disastrous). Also, ensuring that the links see pure tension/compression loads (no bending) will minimize loading on the threads (probably the weakest area) so joint design is important.