Sounds like a great project! Automated window coverings is the first thing on my personal “someday, if I win the lottery” home automation list. 
A smart app is actually the easy part here: just use Core or Webcoreyou should eventually be able to set up any kind of schedule that you want.
The tricky part is what will be the physical device that controls your shades.
You said you want to use your existing shades? We would need to know more about their current design. And are your existing shades already motorized? In that case we need to know the exact brand and model.
Starting from Scratch
If you wanted to buy new shades, you could get either Lutron Serena shades or Graber Shades from zebra blinds and have a quite simple installation with very good SmartThings integration. But in both cases you would be starting from scratch, neither can be used to retrofit existing window coverings.
If you have an existing remote
If your existing shades are already motorized and they have a handheld remote with buttons, sometimes the easiest way to integrate it with SmartThings is to add a Naran Push microbot, which is a “robot finger” which does nothing except push a button on command. But it can be used to integrate existing handheld remote or wall mount control panels with echo, smartthings, IFTTT, etc. I use these at my own house and really like them because they let me solve some retrofit use cases that just can’t be easily solved any other way. They don’t require any wiring and they don’t damage the existing remote. But they are expensive, and $49 for each microbot $89 for a bridge to connect them to the Internet (one Bridge can support up to 40 micro bots). Still, when you’re looking at window coverings, the cost may be comparable to any of the other solutions and it let you keep all the existing safety features of the current remote. So it is something to consider.
Adding a motor to existing shades
If you don’t use the microbot and you want to use your existing shades and they are not motorized then you have to look at adding some kind of Motor system as well as a radio device to communicate with SmartThings. It can often be done, and there are community members who have done it. But it gets complicated and expensive.
See the project reports section of the quick browse lists in the community – created wiki and look on the shades and window coverings list and you can read about what other people have done.
Sensors and weather information
As far as the trigger variables you want to use like sun, wind, etc. you’re going to have to add some sensors or use a weather reporting system to get that information so you can then feed it into webcore. There are a number of different options for this but we can get to the sensor discussion after you’ve looked at some of the shade control options.
Oh, and here’s the information on Core. Again, it’s the smartapp that should be able to handle any rules you want to set up: