Assuming you are not a programmer, you are probably not going to write your own platform. That is a major undertaking even for an experienced programmer. So the question becomes what platform are you going to use and what language does it support? If this is correct, maybe others can point you to a list of platforms with the language they support and you can evaluate them to see if they meet your needs.
As for C# vs. Java:
They are very similar.
They have similar (very good) performance.
You have a lot of choice for tools in Java. Microsoft does a great job with tools for C#.
C# is much more prevalent on consumer (Windows) desktops and therefore may be used as a language for more consumer trading platforms, so this may be the way to go for you.
Java is much more prevalent in industry, including the financial industry.
Java has a much larger community and many more free and open source libraries available, though this may not matter for what you need to do.
Who do you like more, Microsoft or Oracle? OK, this doesnât matter. Oracle bought Sun (the inventors of Java) because most everything they write (middleware, tools, etc.), except the database itself, is written in Java.
If you are going to write your own platform check to see what languages your data provider and broker APIs support.
Bottom line: If you want to be a programmer in the financial industry, Java, otherwise, see the first paragraph (probably C#).
I chose Java because I wrote my own platform and didnât want to have to run on Windows (though I still do).