You have to have one of the object types in your list to make rain.
You also need to break this down a bit, you have a lot of requirements there...
1. Rain. It's usually done using a plain, or series of plains for the simplest implementation. You can also use a particle system, there are a few around on the forums (quite old posts), or the Particles Pack for DB pro.
2. Texture Splats. Again, plains are good. You need to make a "system" that places them at random, fades them in and out, and also scales them. It's not a simple thing to do, and will need some thought.
3. Puddles. Depends what effect you are trying to acheive. You could use a rising plain, or be creative with a reflective shader that changes over time.
What you are trying to do is actually quite complex. Look at some commercial games, and you'll soon realise that not many get weather systems right, and lots don't have a weather system at all.