I totally agree on the whole "Starfleet isn't the Military" issue. Overtly militant fan designs are a huge pet peeve of mine! Can't stand the bloody things and don't get me started on "Starfleet Marines"!. Still, allot of Starfleet's tradition, hierarchy and terminology clearly has it's roots in old Earth military. More so than I would prefer, but we're stuck with it.
As far as the "ships stores" go, I don't think they are stores in the sense that K-Mart is a store. As I said I live on a British Army camp (and future concentration camp for those who've seen V for Vendetta ;0)) and like allot of civvies in the area I have worked for the Army as a civil servant and over here, when someone refers to "Stores" they're not talking about where they get their crisps, paper and mars bar. Stores are, well, for storing things. A signal stores is where the radio equipment go and are checked out from, accommodation stores are for furniture and so on; all of this of course coming under the QM's department. Having said all that, I'm not sure if the same applies to the Navy or indeed any American armed forces, this is just based on my own experience.
Anyway, in this context I'd say ship's stores would be where equipment, uniforms and whatever is in the cargo bays is checked out from. In the context of the 23rd century they also seam responsible for fabricating item from the ship's database (e.g. 20th century clothes & artefacts) and of course recycling when they're finished with.
As for bringing civilisation to the frontier, I'm sure they'd be stocked up on the essentials for 23rd century colony building (survival gear, medical supplies, shelters, food & water packs, survey equipment, agricultural tools, construction equipment, computers, etc) I just have a hard time seeing Starfleet bringing snow globes and fridge magnets to the colonists on Caldos II.
However, I'm sure as a courtesy a ship's captain might allocate a certain amount of resources to personal items for the colonist, like say toys for the children, some hard copy books for the town library, perhaps some sports and leisure gear or some meditation lamps for the Vulcan temple.
Still, we're given to believe that the Federation is not materially driven, so I can't see them specifically having a gift shop. I'm sure that need is taken care of by whatever the 23rd Century inheritors of the old Earth Cargo Service (which seamed mostly a franchise endeavour) might be or indeed independent traders like Mudd & Jones.
On the watch front, I also have four. Two digital & analogue, one just digital and one just analogue. The analogue one is what I'd call a "dress" watch, for the odd occasion when I'm required to look smart, the digital is just an old one I keep as a backup while one of the combies is a cheepo "don't care if it gets smashed to buggery" watch I used to wear when I worked on building sites, the other one being my everyday watch, but it's one of those that you can turn off the digital face so it looks analogue.