One thing you will notice with both walnut and mahogany is that they are both open grained woods. This means that if you want a "piano finish", that is, a smooth finish without indentations following the grain. you will have to apply many coats with some sanding between to level the low spots. I have streamlined the process by rubbing the finish when it is almost dry. This pushes the thickened material into the cracks, cutting down on the number of coats necessary.
Of course some prefer the effect of the grain texture telegraphing through. It makes it look more like real wood, not a picture under a layer of plastic. In this case, the trick is to have a uniform amount of grain texture exposed over the entire surface.
The high humidity can be an issue. Keep the coats light and you may try using a fan between coats. The downside is it exposes the drying finish to more dust, but it evaporates the solvents much quicker than still air. Urethanes don't blush (turn milky) as readily as lacquers in high humidity, so that shouldn't be an issue.
It's not as complicated as the suggestions make it appear and if something goes wrong, well that's what sandpaper is for.
