Try it out. Implement the entire site in Perl, then find out which parts are taking too long. Then see whether you can find a faster Perl solution (maybe PDL is suitable for your problem space) or whether you need to reimplement parts in another language. Embedding C finctions into a Perl module is documented well enough that it should be easily possible to change the number-crunching aspects of even a complex app from one to the other.
This gives you a working (albeit possibly too slow) solution in the minimum period of time, and you can improve the parts that need improving as you go. At worst (if for some unlikely reason it turns out you need to do the entire site in C or C++), the initial Perl solution is a good prototype. You always learn when you do something for the first time, and Perl is well suited for rapid prototyping.