Filter recommendations for Fujinon GF lenses?

I do use a protection filter on each of my lenses.  I'm very often in salty, sandy places, sometimes with so much wind blown salty moisture in the air that I pull the camera out, take a hasty photo and replace it back in the bag as quickly as I can.  I've been known to lick tiny crystals of salt off the front of the (protected) lens on rare occasions.

So yeah, Hoya HD Protector filters for me all around and permanently installed.  I did a few with/without comparisons some time ago and concluded that if there was a difference (debatable) it certainly wasn't enough for me to concern myself over, others may disagree.

I also have and use ND filters in 3, 6 and 10 stops and a circular polarizer, all Hoya.   I use filters for the biggest thread diameter needed and step up rings for any smaller thread lenses.  I don't use hoods at all, I prefer to use my hand when needed.

Yes, your lens caps will fit right onto a screw in filter in the same way as usual.  Step up rings will almost always get in the way of however a hood mounts and the two are rarely compatible.