You don't "have" to put 3 occupations - you "can" put up to the 3 occupations on your application.
I can't speak to PAO or IntO, but for LogO and HSM no matter what uniform you wear you're not necessarily going to be stuck on ship.
I've just surpassed my 5 year mark as an HSM, I also wear the Naval uniform. LogO's and HSM's (again can't speak on the other two) are considered purple trades in that although you're wearing one specific uniform you can be posted to any base.
Although rumour mill is it that they're changing their training, to reach qualification (OFP) you have to do BMOQ, BMOQ(L), Common Logistics Course, Logistics-Army/Navy/Air Force (as appropriate), then the Army and Air Force require one specialty Log course, the Navy requires two different courses (HR and Finance if memory serves me, but I might be wrong on which two).
HSM requires BMOQ, BMOQ(L) [same as LogO]; Common Health Services Officer Course (5 days of online training); and the RQ-HSM-Lt course which is approximately two months. As an HSM you can wear any environmental uniform - but for the most part the occupation wears the Army uniform - very few Air Force or Navy in the occupation.
As to how I enjoy it - so far it's been the best 5 years of my career (and I'm in my 27th year of service now). My 5 years have been spent in an office environment, but that's because of my background as a RMS Clerk [HRA] and becoming an expert in administration and finance; but there are also clinic roles and operational roles. I love the occupation, I love my peers, my chain of command is amazing. Just like any job I have my days where they aren't so great - but the good days far out number the bad days. I had the choice of going LogO or HSM in 2021 and I'm very happy that I went with HSM.
Don't hesitate to reach out via DM (or continue to ask here).