My suggestion would be:
RhinoCommon is a library accessible easily accessible from C#, Python, and VB.NET.
Grab a copy of MS Visual Studio Community edition (free to individuals, possibly not if you’re doing this directly for your company rather than learning a skill on your own time).
Spend a few hours trying out C#, VB.NET and Python. Run the hello world programs. Walk through a few tutorials with objects. During this period, basically ignore Rhino: you’re trying to see which of the three feels most natural to think in. For power, they’re all approximately equivalent. Until you get to a more advanced level, C# and VB.NET are basically functionally equivalent but just written in different styles and Python is a completely different thing.
You can really get inside of the geometry details with C++, but since you’re also apparently on your first text based programming language the learning curve would be much steeper: you want a problem like “Hmm, I tried to move a box and it disappeared; how do I fix that?” not “Rhino just disappeared and I have no idea why.”
C#/VB.NET have better integration into Microsoft’s development tools IMO, which might also be important if you want to write a tool that does something like bridging to Excel or Word. Python has an impressive set of libraries.
Don’t worry too much about your choice. For your first language “help, I’m drowning in punctuation!” (C#) or “wait, white space means something?” (Python) are perfectly valid reasons to pick something that minimizes the learning curve. That said, C# and Python seem to be most popular by a big margin in the discussion forums over VB.
Start browsing around https://developer.rhino3d.com/.
Download the Developer samples from McNeel. mcneel/rhino-developer-samples: Rhino and Grasshopper developer sample code (github.com). There are more resources one directory up. Those samples favor C#/VB.NET, but the online resources under developer.rhino3d.com are sometimes superior for Python. The guide to using Eto is an example (library so your UI will work on Windows and Mac).
The “your first plugin” type starter guides, also under developer.mcneel.com, are then great, whether or not your ultimate goal is to write a plugin: they and the developer samples will show you how to connect to Rhino.
From there, ask questions about things you don’t understand.