For the future, it's often really helpful to understand how the instrument works, which can help in making and designing it.
Thus in your case, once you know the top is the main producer of sound, you know that this requires the most thought.
The top works by taking the energy in the strings and turning it into vibrations in the top, which move the air to make sound. So, fairly obviously, this tells you three things:
1. If the top is too stiff it won't move much, so it won't make much volume. If it's floppy it is unlikely to make a nice sound (think cardboard).
2. If the top is too heavy, you get the same result.
3. If the top is too flexible the uke will fold in half when strung up.
So you want a top which is light, stiff but flexible.
Bracing and bridge plate and bridge all add to the mass of the top, so you need to keep these light (OK, bridges can be too light but that's the advanced course, and for a uke it's hard to make a bridge too light!). So you want the lightest possible wood which is stiff enough to work as a brace - as many have said, spruce fits the bill well. Mahogany is heavier for the same stiffness.
The bridge plate is a brace, but also stops the strings from pulling through. Spruce dents easily, mahogany less so. So this suggests mahogany (or similar), but very thin. If you don't use a pinned bridge then you don't have to worry about the strings pulling through, so spruce again.
Top thickness needs to give you stiff but flexible after you've added the bracing and patch, so you thickness it accordingly. Any numbers you read are just rough starting places, because each piece of wood differs even from consecutive cuts from the same plank. So flex your top when thinning it to decide where to stop. If you are more scientific/engineering minded, measure its deflection under a known load to decide when it's the right thickness.
Good luck with future builds!
