If you reload, I would definitely go with a 7wsm. It is more powder efficient and you can get some impressive velocities with the heavy 7mms.
The argument for 7rm is the it is more common available, but to me that doesn't matter because I reload.
The powder difference and loading in a short mag narrowed it down to the 7wsm fairly quickly for me.
7saum just doesn't have as much case capacity to keep up in a short action, in my opinion, but shines with better powder efficiency in a long action. Brass is more consistent than the 7wsm, but really hard to find and much more expensive. I weight sort and neck turn my 7wsm brass and get great sub-MOA accuracy at a fraction of the cost. Plus until recently I could just go to my local store and pick up some 7wsm brass, not to same with 7saum
I agree that a long action will allow you to get more velocity out of any 7mm mag, and it will depends on your barrel length and preferences.
I have a surgeon RSR, which is a short action with mag bolt face. I use Alpha mags but Seekins are great too. For the 180 Berger hybrids & hunting VLDs, I'm getting 2950fps with a mid-range H1000 load from a 28" barrel. You can run the numbers on a ballistics calculator and make a decision for yourself.
If you have a Stiller long action, just keep it and use of for a 7wsm.
My 7wsm makes 1000 yds hits on a chest-sized plate easy.