I have no prior experience with dedicated software for stiching or focus stacking. What is worth trying?
Depends on your requirements. Photoshop and Lightroom have some capabilities for stitching and stacking, but offer little control of the process, and Photoshop uses lots of memory.
For dedicated Stitching, PTGUI (Pro) is the way to go. 'Hugin' can also produce excellent results.
For dedicated FocusStacking, Helicon Focus or Zerene Stacker, both produce excellent results.
These programs offer so many features, that it can take a while to master them all.
Starting with properly made images for the intended purpose, helps a lot.
Cheers,
Bart