Dave,
Getting a smooth paint finish without an airbrush may not be easy, but I think it can be acheived with practice. A sprayed primer should help the brushed paint to settle more smoothly, as it should bond evenly to the smooth primed surface, and a neutral colour (probably grey) would be the best. For brushes, I've found a wide flat brush with soft bristles can give the smoothest coat finish for covering large areas, although others may have differing views on the best brushes. The paint consistency needs to be fairly fluid but not too thin, it's worth spending a bit of time stiring and preparing the paint before starting. Neat edges between colours are important for the final item to look good, which can be done with a steady application or masking tape. Smaller details are ok with normal smaller modelling type brushes.
For assembly, I normally assemble into modules before painting, so that it is easy to get the brush everywhere required, but smaller details will already be attached to each module for painting, to improve blending the smaller parts in.
We could look at other tips, such as choosing the wood deck colour carefully, as the wrong shade of brown wouldn't look too good, and if weathering, normally rust streaks run vertically down from a small rusty point in a corner or exposed point on the hull (looking at photos of ships quickly highlights likely points), but should be done subtly, and can be added in a variety of ways, from brown pencil crayon, to pastel powders or paints.
Anyway, always happy to share tips I've picked up along the way.
Rob