Sailing ship modeling is a litte different from most other facets of the hobby, in that there are several widely-accepted approaches to it. Some ship modelers follow the same basic principles that airplane, armor, and railroad modelers usually do: they attempt to reproduce the prototype as accurately as possible in all aspects, including finish. A modeler of that pursuasion will paint everything that was painted on the real ship, and make the model look as authentic as he/she can.
Another approach compromises with literal authenticity a bit for the sake of aesthetics. Some ship modelers like to let the colors and textures of the wood speak without hindrance, and shun paint. Such models aren't literally accurate, but when well executed can be really beautiful. It's a matter of taste.
One of my predecessors at the maritime museum where I used to work claimed that Type A was the only legitimate way to build a ship model. He claimed Type B models had no place in a museum because they weren't accurate representations of the real thing. I disagree. To me, that argument makes about as much sense as asserting that all photographs should be taken in color, because black-and-white pictures aren't realistic.
I haven't built the MS kit you're working on, but that firm's products tend to be aimed primarily at Type A modelers. I assume most of the parts are basswood - a good, reliable modeling material, but not the best-looking wood for staining. For what little it's worth, if I were building that particular model I'd probably paint those parts that were painted on the prototype, and stain the deck planks to make them look like the original bare wood. Olympic makes a stain color called "Driftwood" that, to my eye, is about right. (I'd also suggest - though the instructions may cover this - running a soft pencil around each of the deck planks. The resulting fine, dark grey lines are a good representation of deck caulking.)
One more tip. Your concern about splashing paint (and other stuff) on the deck is entirely justified. My suggestion is to get a can of white shellac (make sure it's fresh; shellac goes bad if it sits in the can too long), dilute it almost beyond recognition with denatured alcohol, and apply a coat of it to the deck. It will be almost invisible, but will protect the deck from accidents.
The bottom line is that it's all up to the individual modeler. Good luck. It's a great hobby.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.