When running the TPI tool in SAGA, I get this parameter-entry window:
Under the section highlighted in the red box, what do these parameters mean? Do the search/neighbourhood grouping parameters mean cells? What would the "standardize" section indicate? Would distance weighting also be recommended?
It is good you started to work with TPI on SAGA, since it is rare software which cares TPI's scale-dependent nature. In the poster linked below you will find answers.
Andrew D. Weiss Topographic Position and Landforms Analysis
The above poster is in fact accessible from inside SAGA. On SAGA Manager Window, you would have already run Topographic Position Index (TPI) through Tool Libraries | Terrain Analysis | Morphometry. Then you can see Description on Object Properties Window which shows parameters setting, along with referenced papers including the link to the above A.D.Weiss poster.
Then remaining question would be Distance weighting. My personal recommendation is not to use it. More important part is how to find best scale (outer radius and inner radius; like a doughnut) which describes your subject best. Adding distance weighting complicate its interpretation and can be distracting.
Menu | Map | Save as Image), not your TPI grid. You can try (1) Save it as SAGA Grid by Manager | Data | Grids Right-click on your TPI Grid and Save As TPI.sgrd. (2) Convert sgrd file to asc by Menu | Geoprocessing | File | Grid | Export | Export ESRI Arc/Info. If this does not work, please open a new question.