Considering the large size of the house, you will need a larger softener. Wait until you close on the house and post more information for us to make a recommendation.
The reionator has some Anion resin in it. This will have little affect on the water quality unless you are trying to remove tannins, sulfates, nitrates, etc. Does your water have this? If it is a municipal water system then probably not.
Non salt systems work completely different than salt based systems, and most of the professional on this forum are probably going to recommend a salt system due to our many years of experience with both system designs.
We would need to start:
Pipe size of the main line where the softener is to be installed.
Municipal or well water (your own well, not if the municipality uses a well)
Water hardness (your city will have a water report available online or you can call them and ask them)
If you have your own well, then you will probably be required to have a new test done, that will include all of the information we need.
Good luck on the new house, and congrats on moving to San Antonio, it is a beautiful town. I visit there a couple times a year and always enjoy it!
I can refer you to many great companies in that area that will give you an excellent price if you want.