I think this is a photo of my Grandfather. I think the photo was taken in Britain. The family story is that he had a "good war" He was a gamekeeper and farm manager and was retained on the staff of some Uk based officer.
The cap badge looks like a globe surrounded by a wreath. That would make it the Royal Marines, BUT it should have a lion & crown above it. They could be being obscured by the cap however. I'm presuming 14-18, is that correct?
Pteranadon...Definitely Royal Marines, but like others not sure which branch? I can't tell you what it is, but can tell you what it isn't. The RM Arty badge of the time was different to the regular RM badge (explanation below). I would think the LI branch would be most likely judging by the size of the fold covering the top of the badge, but that's just guesswork. Sorry i can't be more helpful, and good luck with the search.
Kabulronin...You're quite right that RM was indeed split into various roles. The RMLI had the normal badge, surmounted by the LI bugle as shown by Brandysoured. But they also had their own RM Artillery which would explain the shore batteries you refernced. The post 1922 badge was again the normal RM badge, surmounted by a Bomb exploded proper (7 flames) where the wreath meets. However, the pre 1922 badge of the RM Artillery, did not have the globe and wreath, but was similar in appearance to that of the Grenadier Gds O/Rs, but with only seven flame bursts.
Edited to add...Nice post Smudger, i hadn't seen that before.