Start with Python; its way more forgiving if you’ve not coded before and just want to have scripting skills you can mix into your day job. Ultimately, knowing both will give you the most flexibility; its important to know that the right tool for the right job also applies with programming languages. Plus, if you learn one, you’ve pretty much learnt the other, at least from a conceptual standpoint. You don’t need C# to access the Revit API either; IronPython is .NET enabled and the syntax for making Revit API calls is practically identical to C# just less verbose (so you could argue, better for getting started). There are some nuances where this rule of thumb doesn’t apply, but they are few and far between.
The main advantage with C# is the fact you can develop in a full IDE, which is ideal for developing complex programs or solving complex (design?) problems. Paradoxically, its also the ‘easiest’ option for developing by virtue of the IDE, the catch being you need to understand basic comp-sci paradigms and the language of course, before you can do anything useful with it. Python on the other-hand has a reasonable text editor, which can be improved with stubs (which emulates IntelliSense in Visual Studio), but you cant really compare the two as its really just a halfway-house at best.