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C will be the natural choice as wide open-source code-base is readily available.
Legacy solver code-base will be in Fortran and it can successfully and automatically converted to "C".
When starting to write new or improve the existing code-base try these;
1) Use C++ for better OO.
2) Use Python as it is much easier and equally good is performance (cpython).
3) Preferably look at server-side technology (node-js for eg) so that you target web-complaint software right from the inception.
-YD