Welcome to APUG Erik,
A medium speed film (ISO 100-200ish) like FP4+ will work great as long as you are comfortable with larger apertures (shorter DOF) when it gets darker. 1/125 at f4 is a decent setting for say open shade, 1/60 at f4 will probably work fine for you in full shade.
If you want smaller apertures (longer DOF) or faster shutter speeds a high speed film (ISO 400 up) may be a better choice. I wouldn't worry to much about overexposing films like HP5+ (or Tmax 400, Delta 400...).
These films are pretty flexible. Personally I'll expose these 400 speed films happily at EI ratings down to 50 to sneak in at 800 for some shots. For FP4+ I happily shoot down to 25 and up to 200 if needed.
Pan F would be a great choice if you like short DOF mid day.