Stiff paper isn't going to work so well if you have details like ladders and watertight doors to raise it off the surface a bit.
An air brush isn't necessary, but I find it makes the work easier and quicker. I can't paint straight enough to do these patterns without masking, and I can cover larger areas with finer paint quicker with an airbrush than a brush paint. There are those with skills to brush paint without brush marks and excellent coverage, but I'm not one of them.
There is no easy "shake the box and a complete kit comes out" method for ships. I find it easiest to paint the vertical surfaces first and then do the decks. When you have curved structures (such as Bismarck's circular cut-outs in the superstructure for her medium guns to turn in) it's just easier to mask the vertical bulkhead with a straight piece of tape than it is to measure and cut the right circle to cover the deck first.
So, I paint the vertical surfaces first, including all camouflage colors if I'm doing dazzle. Then, I mask off the superstructure and deck pieces that are maskable and start in on the deck. Some deck details I can't mask well and will either hand paint later or mask the deck after it's done and go back to paint the vertical colors on. An example of this would be the deck chocks, which are an odd shape that doesn't mask well. However, the flat deck around them does, so I'll generally plan on coming back after the deck is done to get them painted.
When doing the deck or vertical colors, keep in mind that you don't HAVE to do it all in one setting. To protect from over spray, I may mask off and paint one little platform deck in one area, and then a couple of other one spread out. You can arrange your tape to do it all at once, but I just find it more manageable to break it up into smaller pieces of work.