OK, you will need to use the iPhone with the “SmartThings classic” app.
I’m not quite sure what you’re referring to about “web control,” but the IDE, which is the web interface to your SmartThings account, will work through just about any web browser, so that should be OK. You can even use it through Safari on your iPhone, although the tiny screen is hard to work with.
Start by reading the FAQ on custom code. It will explain the terminology and the basic concepts.
Then go to the community – created wiki, and look on the quick browse lists in the DTH section for the lists for “remotes and buttons” or maybe the list for lighting. Anyway, one of those should have at least one custom DTH for the devices you were looking for. (This paragraph will make more sense after you’ve read the FAQ)
Then just go to that thread and follow those instructions. If you have any problems, ask follow on questions in the thread where you get the code. 
Once you have the right DTH and the device assigned to it, the buttons will appear in the official smartlighting feature, and webcore, and in many other smart apps which support button controllers.